objective: students will be able to understand the basics concepts of geometry and be able to apply...

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Accelerated Math Geometry Unit Objective: students will be able to understand the basics concepts of geometry and be able to apply them to real world problems.

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Accelerated Math Geometry Unit

Objective students will be able to understand the basics concepts of geometry and be able to

apply them to real world problems

AnglesTrianglesCircles3-D ShapesAreaVolumeSurface Area

Topics we will coverhellip

Letrsquos Get Started

Angle and line relationships

Objective to be able to examine relationships between pairs of angles examine

relationships of angles formed by parallel lines and a transversal

Key concept pairs of angles

Vertical Angles

When two lines intersect they form two pairs of opposite angles

Angles are congruent

Model

41

23

1 23 4

ampamp

Symbol

1 2

Key concept pairs of angles

Adjacent Angles

When two angles have the same vertex between them share a common side and do not overlap

Model

41

23

1 33 2

ampamp

Symbol

1 3ampare adjacent angles

Key concept pairs of angles

Complementary Angles

When two angles have the sum of 90o

Model

35o

65o

Symbol

35o + 65o = 90o

Key concept pairs of angles

Supplementary Angles

When two angles have the sum of 180o

Model

35o

145o

Symbol

35o + 145o = 180o

Key concept pairs of angles

Perpendicular Lines

When two lines intersect to form a right angle

Model

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

AnglesTrianglesCircles3-D ShapesAreaVolumeSurface Area

Topics we will coverhellip

Letrsquos Get Started

Angle and line relationships

Objective to be able to examine relationships between pairs of angles examine

relationships of angles formed by parallel lines and a transversal

Key concept pairs of angles

Vertical Angles

When two lines intersect they form two pairs of opposite angles

Angles are congruent

Model

41

23

1 23 4

ampamp

Symbol

1 2

Key concept pairs of angles

Adjacent Angles

When two angles have the same vertex between them share a common side and do not overlap

Model

41

23

1 33 2

ampamp

Symbol

1 3ampare adjacent angles

Key concept pairs of angles

Complementary Angles

When two angles have the sum of 90o

Model

35o

65o

Symbol

35o + 65o = 90o

Key concept pairs of angles

Supplementary Angles

When two angles have the sum of 180o

Model

35o

145o

Symbol

35o + 145o = 180o

Key concept pairs of angles

Perpendicular Lines

When two lines intersect to form a right angle

Model

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Get Started

Angle and line relationships

Objective to be able to examine relationships between pairs of angles examine

relationships of angles formed by parallel lines and a transversal

Key concept pairs of angles

Vertical Angles

When two lines intersect they form two pairs of opposite angles

Angles are congruent

Model

41

23

1 23 4

ampamp

Symbol

1 2

Key concept pairs of angles

Adjacent Angles

When two angles have the same vertex between them share a common side and do not overlap

Model

41

23

1 33 2

ampamp

Symbol

1 3ampare adjacent angles

Key concept pairs of angles

Complementary Angles

When two angles have the sum of 90o

Model

35o

65o

Symbol

35o + 65o = 90o

Key concept pairs of angles

Supplementary Angles

When two angles have the sum of 180o

Model

35o

145o

Symbol

35o + 145o = 180o

Key concept pairs of angles

Perpendicular Lines

When two lines intersect to form a right angle

Model

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Angle and line relationships

Objective to be able to examine relationships between pairs of angles examine

relationships of angles formed by parallel lines and a transversal

Key concept pairs of angles

Vertical Angles

When two lines intersect they form two pairs of opposite angles

Angles are congruent

Model

41

23

1 23 4

ampamp

Symbol

1 2

Key concept pairs of angles

Adjacent Angles

When two angles have the same vertex between them share a common side and do not overlap

Model

41

23

1 33 2

ampamp

Symbol

1 3ampare adjacent angles

Key concept pairs of angles

Complementary Angles

When two angles have the sum of 90o

Model

35o

65o

Symbol

35o + 65o = 90o

Key concept pairs of angles

Supplementary Angles

When two angles have the sum of 180o

Model

35o

145o

Symbol

35o + 145o = 180o

Key concept pairs of angles

Perpendicular Lines

When two lines intersect to form a right angle

Model

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Key concept pairs of angles

Vertical Angles

When two lines intersect they form two pairs of opposite angles

Angles are congruent

Model

41

23

1 23 4

ampamp

Symbol

1 2

Key concept pairs of angles

Adjacent Angles

When two angles have the same vertex between them share a common side and do not overlap

Model

41

23

1 33 2

ampamp

Symbol

1 3ampare adjacent angles

Key concept pairs of angles

Complementary Angles

When two angles have the sum of 90o

Model

35o

65o

Symbol

35o + 65o = 90o

Key concept pairs of angles

Supplementary Angles

When two angles have the sum of 180o

Model

35o

145o

Symbol

35o + 145o = 180o

Key concept pairs of angles

Perpendicular Lines

When two lines intersect to form a right angle

Model

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Key concept pairs of angles

Adjacent Angles

When two angles have the same vertex between them share a common side and do not overlap

Model

41

23

1 33 2

ampamp

Symbol

1 3ampare adjacent angles

Key concept pairs of angles

Complementary Angles

When two angles have the sum of 90o

Model

35o

65o

Symbol

35o + 65o = 90o

Key concept pairs of angles

Supplementary Angles

When two angles have the sum of 180o

Model

35o

145o

Symbol

35o + 145o = 180o

Key concept pairs of angles

Perpendicular Lines

When two lines intersect to form a right angle

Model

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Key concept pairs of angles

Complementary Angles

When two angles have the sum of 90o

Model

35o

65o

Symbol

35o + 65o = 90o

Key concept pairs of angles

Supplementary Angles

When two angles have the sum of 180o

Model

35o

145o

Symbol

35o + 145o = 180o

Key concept pairs of angles

Perpendicular Lines

When two lines intersect to form a right angle

Model

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Key concept pairs of angles

Supplementary Angles

When two angles have the sum of 180o

Model

35o

145o

Symbol

35o + 145o = 180o

Key concept pairs of angles

Perpendicular Lines

When two lines intersect to form a right angle

Model

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Key concept pairs of angles

Perpendicular Lines

When two lines intersect to form a right angle

Model

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Example 1

Jan is cutting a corner off a piece of rectangular tile Classify the

relationship between angle x and angle y

If the m y = 135o what is the measure of x

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are

on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6

Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8

Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6

214

758

6

3

Parallel Line

Parallel Line

Transversal Line (a line that intersects two parallel lines

When a transversal intersects it forms 8 angles Interior and exterior angles

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Example 2 (page 496 in book)

Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5

Since angle 3 and angle 5 are alternate interior

angles they are congruent

b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3

Since angle 1 and angle 5 are corresponding angles they are

congruent and angle 5 measures 120 degrees

Since angle 5 and angle 3 are congruent angle 3 measures

120 degrees also

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Example 3 (page 496 in book)Using the figure in the book answer the following questions

Measure of angle ABD = 164o

Find the measures of angle ABC and CBD

(2x + 23)o Xo

A

C

D

B

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Do Some Guided Practice

Open Your Books

Way to Go

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying

Triangles

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

All Triangles Have 3 Names

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

First MiddleLast

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Letrsquos look at the first nameshellip

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

First Names

ACUTE

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Acute

3 acute angles that measure less than 90o

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

First Names

OBTUSE

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Obtuse

1 obtuse angle that measures greater than 90o

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

First Names

RIGHT

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Right

1 right angle that measures 90o

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Letrsquos look at the middle nameshellip

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Middle Names

SCALENE

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Scalene

No equal sides

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Middle Names

ISOSCELES

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Isosceles

2 equal sides

Shows that the sides are of equal length

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Middle Names

EQUILATERAL

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Equilateral

3 equal sides

Shows that the sides are of equal length

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Letrsquos look at the last namehellip

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Last Name

TRIANGLE

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Letrsquos look at some exampleshellip

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Obtuse Scalene Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Acute Isosceles Triangle

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

What is the full name of this triangle

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Acute Equilateral

Triangle

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Looking Good letrsquos playhellip

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Awesome Job

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

NAME THAT TRIANGLE

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Here are some simple rules Everyone will be in teams chosen by the teacher

Everyone will have a turn at writing the answer

Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND

Negative comments will result in loss of points

Talking DURING rounds will result in loss of points

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

LETrsquoS PLAY

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

AcuteEquilateral

Triangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

ObtuseIsoscelesTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

ObtuseScaleneTriangle

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

20191817161514131211

10987654321

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

RightScaleneTriangle

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Name That Triangle

GREAT JOB EVERYONE

Do we need a tie breaker

>

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Letrsquos find the measures of

triangles

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

All triangles measure

180o

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

What do they measure

180o

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

71o

64o

X

Letrsquos find x

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

71o

64o

X

64o + 71o = 135o

180o - 135o = 45o

x = 45o

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

38o

Letrsquos find x

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

38o

90o + 38o = 128o

180o - 128o = 52o

x = 52o

X

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Now find the measures of the

triangles

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

40o

Letrsquos find x

X

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

40o

X = 50o

X

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

40o

Letrsquos find x

X 25o

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

40o

X = 115o

X 25o

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

60o

Letrsquos find x

X60o

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

60o

X = 60o

X60o

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Classifying Triangles

Letrsquos put our new information to the test and start our

assignment for the day

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circle Time

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Parts of a Circle

RadiusDiameterCentral AngleChordSemi Circle

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Radius

What is it A segment that

connects the center point of a circle to the circumference of the circle

A

B

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Radius

How do you name it You name a radius like

a line segment starting with the center point first

Example ABA

B

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Diameter

What is it A segment that

passes the center of a circle and has both endpoints on the circumference of the circle

BC A

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Diameter

How do you name it You name a diameter

just like a line segment do not name the center point

Example CB or BC B

C A

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Chord

What is it A segment that has

both endpoints on the circumference of the circle

C

B

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Chord

How do you name it You name a chord just

like you would a line segment

Example BC or CB

C

B

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference amp Area

Objective to be able to use the formulas for circumference and area to solve real world

problems

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

What is Pi

prodIntro to Pi Video

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Pi

prod = 314159hellip

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Pi

Pi is an irrational numberMeaning it goes on forever and never repeats

So far mathematicians have discovered over 134 million digits of pi

Theyrsquore still working to find morehellip

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Pi

But all you need to know ishellip

prod = 314

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Pi

Pi is a ratio of circumference (C) to diameter (d)

Cd = prod

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference

Circumference is the distance around a circle

Circumference is measured in units

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference

C = (d) prodor

C =(2) (r) prod

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference

Find the circumferencehellip

C = 10 bull 314

C = 314 m

10 m

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference

Find the circumferencehellip

C = 2 bull 2 bull 314

C = 1256 in

2 in

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference

Find the circumferencehellip

C = 2 bull 8 bull 314

C = 5024 yd

8 yd

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference

Find the circumferencehellip

C = 2 bull 314

C = 628 cm

2 cm

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference amp Area

Great Now letrsquos move on to area

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Area

Area is the number of square units that fit inside a circle

Area is measured in units2

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Area

A = prod r2

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Area

Can also be writtenhellip

A = prod bull r bull r

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Area

Find the areahellip

A = 314 bull 6 bull 6

A = 11304 km2

6 km

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Area

Find the areahellip

A = 314 bull 4 bull 4

A = 5024 mi2

8 mi

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Area

Find the areahellip

A = 314 bull 15 bull 15

A = 7065 m2

15 m

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Area

Find the areahellip

A = 314 bull 35 bull 35

A = 38465 ft2

7 ft

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference amp Area

Super work

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference amp Area

So how does this apply in

the real world

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference amp Area

Social Studies The circular base of the teepees of the Sioux and

Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit

r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625

A asymp 177 ft2

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference amp Area

Technology Airport Surveillance Radar (ASR) tracks planes in

a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles

r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60

A = 11304 square nautical mi

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference amp Area

Archaeology The large stones of Stonehenge are arranged in a

circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure

d = 30 m C = 30 bull 314

C = 942 m

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circumference amp Area

Way to go

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Objective to be able to find area of composite figures and use that process to solve real life

problems

Area of Composite Figures

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

SquareRectangle

L bull W

Letrsquos review formulas for area

4 ft

7 ft

9 cm

28 ft2

81 cm2

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Triangle

frac12 b bull h

Letrsquos review formulas for area

5 ft

4 ft

10 ft2

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Circle

314 bull r2

Letrsquos review formulas for area

11304 in2

6 in

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Practice

43 m

92 m

1978 m2

725 m

3 m

2175 m2

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Practice

19625 m2

15 m

225 m2

5 cm

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Way to go

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos look at some new formulas for area

Parallelogram

b bull h 5 ft

7 ft

4 ft

35 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos practice the new formula for area

Parallelogram

b bull h 6 ft

12 ft

4 ft

72 ft2

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos practice the new formula for area

Parallelogram

b bull h 25 in

8 in

35 in

280 in2

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

TrapezoidJust a reminderhellipname the only characteristic that trapezoids have

1 set of parallel sides

Letrsquos look at another new formula for area

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Trapezoid

frac12 h(b1 + b2)

Letrsquos look at another new formula for area

4 in

7 in

2 in

11 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

10 in

4 in

6 in

32 in2

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Trapezoid

frac12 h(b1 + b2)

Letrsquos practice the new formula for area

23 in

17 in

9 in

180 in2

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos practice

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos look at composite figures now

Composite Figures are made up of two or more shapes

To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Find the area of the composite figureThe area can be

separated into a semicircle and a triangle

frac12 (314)(r2) for circle

frac12 (b)(h) for triangle

Example 1

6 m

11 m

141 m 33 m+ 471 m2=

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Find the area of the composite figure The area can be

separated into a trapezoid and a rectangle

frac12 h (b1 + b2) for trapezoid

L bull W for square

Example 1

20 m

825 m 400 m+ 4825 m2=

20 m

25 m

13 m

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Awesome Work

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right

Letrsquos try word problems

15 ft

12 ft

4 ft

210 ft2

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Find the area of each shape and subtract

What about shaded areas

4 cm

3 cm

13 cm

7 cm

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos practice

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Volume of Prisms

Objective to be able to find the volume of certain 3-D shapes to solve real world

problems

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

VolumeVolume of a three-dimensional figure is the

number of cubic units needed to fill the space inside the figure

A cubic unit is a cube with edges 1 unit long

1 cm1 cm

1 cm

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Volume To solve for volumehellip

area of the base bull the height

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Volume Measured in cubic feethellip

cm3

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Rectangular Solids

length bull width bull height

LW

H

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Try It

12 bull 6 bull 8 =

Rectangular Solids

576 cm3

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Try Some on Your

Own

Rectangular Solids

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Triangular Prisms

frac12 bull base bull height bull width

H

B

W

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Try It

frac12 bull 8 bull 10 bull 60 =2400 cm3

Triangular Prisms

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Try Some on Your

Own

Rectangular Solids

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Cylinders

314 bull radius bull radius bullheight

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Try It

314 bull 5 bull 5 bull 14 =

Cylinders

14

5

1099 cm3

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Letrsquos Try Some Word Problems

Rectangular Solids

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Volume

A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the

trailer

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Volume

A tent has the shape of a triangular prism From the

floor to the peal is 9 feet The floor is 22 feet wide and 35

feet long What is the volume of the tent

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

Volume

A bucket has a diameter of 20 centimeters and a

height of 15 centimeters What is the volume

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)

You are sooo good

Rectangular Solids

  • Accelerated Math Geometry Unit
  • Topics we will coverhellip
  • Slide 3
  • Angle and line relationships
  • Key concept pairs of angles
  • Key concept pairs of angles (2)
  • Key concept pairs of angles (3)
  • Key concept pairs of angles (4)
  • Key concept pairs of angles (5)
  • Example 1
  • Special Angle Relationships
  • Example 2 (page 496 in book)
  • Example 3 (page 496 in book)
  • Letrsquos Do Some Guided Practice
  • Classifying Triangles
  • Classifying Triangles (2)
  • Classifying Triangles (3)
  • Classifying Triangles (4)
  • First Names
  • Acute
  • First Names (2)
  • Obtuse
  • First Names (3)
  • Right
  • Classifying Triangles (5)
  • Middle Names
  • Scalene
  • Middle Names (2)
  • Isosceles
  • Middle Names (3)
  • Equilateral
  • Classifying Triangles (6)
  • Last Name
  • Classifying Triangles (7)
  • Classifying Triangles (8)
  • Classifying Triangles (9)
  • Classifying Triangles (10)
  • Classifying Triangles (11)
  • Classifying Triangles (12)
  • Classifying Triangles (13)
  • Classifying Triangles (14)
  • Slide 42
  • Classifying Triangles (15)
  • Classifying Triangles (16)
  • Classifying Triangles (17)
  • Name That Triangle
  • Name That Triangle (2)
  • Name That Triangle (3)
  • Name That Triangle (4)
  • Name That Triangle (5)
  • Name That Triangle (6)
  • Name That Triangle (7)
  • Name That Triangle (8)
  • Name That Triangle (9)
  • Name That Triangle (10)
  • Name That Triangle (11)
  • Name That Triangle (12)
  • Name That Triangle (13)
  • Classifying Triangles (18)
  • Classifying Triangles (19)
  • Classifying Triangles (20)
  • Classifying Triangles (21)
  • Classifying Triangles (22)
  • Classifying Triangles (23)
  • Classifying Triangles (24)
  • Classifying Triangles (25)
  • Classifying Triangles (26)
  • Classifying Triangles (27)
  • Classifying Triangles (28)
  • Classifying Triangles (29)
  • Classifying Triangles (30)
  • Classifying Triangles (31)
  • Classifying Triangles (32)
  • Slide 74
  • Parts of a Circle
  • Radius
  • Radius (2)
  • Diameter
  • Diameter (2)
  • Chord
  • Chord (2)
  • Circumference amp Area
  • What is Pi
  • Pi
  • Pi (2)
  • Pi (3)
  • Pi (4)
  • Circumference
  • Circumference (2)
  • Circumference (3)
  • Circumference (4)
  • Circumference (5)
  • Circumference (6)
  • Circumference amp Area (2)
  • Area
  • Area (2)
  • Area (3)
  • Area (4)
  • Area (5)
  • Area (6)
  • Area (7)
  • Circumference amp Area (3)
  • Circumference amp Area (4)
  • Circumference amp Area (5)
  • Circumference amp Area (6)
  • Circumference amp Area (7)
  • Circumference amp Area (8)
  • Area of Composite Figures
  • Letrsquos review formulas for area
  • Letrsquos review formulas for area (2)
  • Letrsquos review formulas for area (3)
  • Letrsquos Practice
  • Letrsquos Practice (2)
  • Way to go
  • Letrsquos look at some new formulas for area
  • Letrsquos practice the new formula for area
  • Letrsquos practice the new formula for area (2)
  • Letrsquos look at another new formula for area
  • Letrsquos look at another new formula for area (2)
  • Letrsquos practice the new formula for area (3)
  • Letrsquos practice the new formula for area (4)
  • Letrsquos practice
  • Letrsquos look at composite figures now
  • Example 1 (2)
  • Example 1 (3)
  • Awesome Work
  • Letrsquos try word problems
  • What about shaded areas
  • Letrsquos practice (2)
  • Volume of Prisms
  • Volume
  • Volume (2)
  • Volume (3)
  • Rectangular Solids
  • Rectangular Solids (2)
  • Rectangular Solids (3)
  • Triangular Prisms
  • Triangular Prisms (2)
  • Slide 139
  • Rectangular Solids (4)
  • Cylinders
  • Cylinders (2)
  • Rectangular Solids (5)
  • Volume
  • Volume (4)
  • Volume (5)
  • Rectangular Solids (6)