warm up 11/30/15 write down one fun thing that you did over thanksgiving weekend; turn to a neighbor...

WARM UP 11/30/15

Write down one fun thing that you did over Thanksgiving

Weekend; turn to a neighbor and share

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PERIMETER

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PerimeterPerimeter is defined as the distance around

an object or shape.

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Rules to find the perimeterRule 1:Measure the length of all sides of the

shape.Rule 2:Add all the measured sides of the

shape.The sum of all the sides gives the perimeter.

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Example: Find the perimeter of the given rectangle.

Perimeter of the given rectangle is = 11 + 5 + 11 + 5= 32 cm

5 cm

11 cm

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Perimeter of squarePerimeter of the shape when all the sides of

the shape are equal = 4 x length of sideExample – Perimeter of square

4 cm

Perimeter of square = 4 x side

= 4 x 4

= 16 cm

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Perimeter Perimeter obeys Commutative property of

addition. Perimeter of the rectangle does not

change if the lengths of the sides are added in a different order.

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Find the perimeter of the hexagon given below.Answer- 18 cm

3 cm

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Important Tips Two different polygons can have the same

perimeter. Perimeter can be calculated only of the

closed figure.

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13 match sticks are used to make a hut on the paper. If each match stick is 3 cm long, what is the perimeter of the hut?

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What is the perimeter of the given figure?a) 36 cmb) 22 cmc) 28 cmd) None of these

5 cm

2 cm

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The perimeter of the figure given below is 152 cm. Find the missing side.

6 cm

40 cm

11 cm

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If each side of the pentagon is 8 cm, what is the perimeter of the pentagon?

copyright@Ed2netLearning,Inc 14

The Perimeter of a small room is 140 feet. If the room is rectangular shape and it is 40 feet wide, what is the width?

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ASSESSMENT

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1. What is the perimeter of the equilateral triangle with side of 8 cm?

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2. How much ribbon is required to cover the outer boundary of the figure given below?

6 cm

4 cm

3 cm

3. If each centimeter of the ribbon costs $0.05, how much does it cost for the ribbon? (problem #2)


4. If the Perimeter of the square garden is 64 cm. What is the side of the square?


5. Lara’s garden is 13 ft long and 9 ft wide. She wants to put a fence around it. How much fencing will Lara need?

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6. How can you find the perimeter of a rhombus if the length of one side of rhombus is p cm?

a) 4 x p cmb) 4 + p cmc) 4 – p cmd) None of these

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7. Find the perimeter of the figure given below (trapezium).

9 cm

12 cm

5 cm

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8. John ran twice around a square park; each side of the square has a length of 7 m. How much distance did he cover?

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9. Find the Perimeter of the given figure.

8 cm

6cm

4 cm

4 cm

2 cm

WARM UP 12/1/15

Solve the following rebus puzzles

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The area of a shape is a measure of how much surface the shape takes up.

Area

For example, which of these rugs covers a larger surface?

Rug A

Rug B

Rug C

Area of a rectangle

Area is measured in square units.

We can use mm2, cm2, m2 or km2.

The 2 tells us that there are two dimensions, length and width.

We can find the area of a rectangle by multiplying the length and the width of the rectangle together.

length, l

width, w

Area of a rectangle

= length × width

= lw

Area of a rectangle

What is the area of this rectangle?

8 cm

4 cm

Area of a rectangle = lw

= 8 cm × 4 cm

= 32 cm2

Area of a right-angled triangle

What proportion of this rectangle has been shaded?

8 cm

4 cm

What is the shape of the shaded part?

What is the area of this right-angled triangle?

Area of the triangle = × 8 × 4 = 12

4 × 4 = 16 cm2

We can use a formula to find the area of a right-angled triangle:


base, b

height, h

Area of a triangle = 12

× base × height

= 12

bh


Calculate the area of this right-angled triangle.

6 cm

8 cm

10 cm

To work out the area of this triangle we only need the length of the base and the height.

We can ignore the third length opposite the right angle.

Area = 12

× base × height

= × 8 × 612

= 24 cm2

Area of shapes made from rectangles

How can we find the area of this shape?

7 m

10 m

8 m

5 m

15 m

15 m

We can think of this shape as being made up of two rectangles.

Either like this …

… or like this.

Label the rectangles A and B.

A

B Area A = 10 × 7 = 70 m2

Area B = 5 × 15 = 75 m2

Total area = 70 + 75 = 145 m2

Area of shapes made from rectangles

How can we find the area of the shaded shape?

We can think of this shape as being made up of one rectangle with another rectangle cut out of it.

7 cm

8 cm

3 cm

4 cm Label the rectangles A and B.

A

B

Area A = 7 × 8 = 56 cm2

Area B = 3 × 4 = 12 cm2

Total area = 56 – 12 = 44 cm2

ED

C

B

A

Area of an irregular shapes on a pegboard

We can divide the shape into right-angled triangles and a square.

Area A = ½ × 2 × 3 = 3 units2

Area B = ½ × 2 × 4 = 4 units2

Area C = ½ × 1 × 3 = 1.5 units2

Area D = ½ × 1 × 2 = 1 unit2

Area E = 1 unit2

Total shaded area = 10.5 units2

How can we find the area of this irregular quadrilateral constructed on a pegboard?

C D

BA


An alternative method would be to construct a rectangle that passes through each of the vertices.

The area of this rectangle is 4 × 5 = 20 units2

The area of the irregular quadrilateral is found by subtracting the area of each of these triangles.



Area A = ½ × 2 × 3 = 3 units2

A B

C D

Area B = ½ × 2 × 4 = 4 units2

Area C = ½ × 1 × 2 = 1 units2

Area D = ½ × 1 × 3 = 1.5 units2

Total shaded area = 9.5 units2

Area of irregular quadrilateral= (20 – 9.5) units2

= 10.5 units2


Area of a triangle

What proportion of this rectangle has been shaded?

8 cm

4 cm

Drawing a line here might help.

What is the area of this triangle?

Area of the triangle = × 8 × 4 = 12

4 × 4 = 16 cm2

Area of a triangle

The area of any triangle can be found using the formula:

Area of a triangle = × base × perpendicular height12

base

perpendicular height

Or using letter symbols:

Area of a triangle = bh12

Area of a triangle

What is the area of this triangle?

Area of a triangle = bh12

7 cm

6 cm

= 12

× 7 × 6

= 21 cm2

Area of a parallelogram

Area of a parallelogram = base × perpendicular height

base


The area of any parallelogram can be found using the formula:


Area of a parallelogram = bh

Area of a parallelogram

What is the area of this parallelogram?


12 cm

7 cm

= 7 × 12

= 84 cm2

8 cm

We can ignore this length

Area of a trapezium

The area of any trapezium can be found using the formula:

Area of a trapezium = (sum of parallel sides) × height12


Area of a trapezium = (a + b)h12


a

b

Area of a trapezium

9 m

6 m

14 m


= (6 + 14) × 912

= × 20 × 912

= 90 m2

What is the area of this trapezium?

Area of a trapezium

What is the area of this trapezium?


= (8 + 3) × 1212

= × 11 × 1212

= 66 m2

8 m

3 m

12 m

Area problems

7 cm

10 cm

What is the area of the yellow square?

We can work this out by subtracting the area of the four blue triangles from the area of the whole blue square.

If the height of each blue triangle is 7 cm, then the base is 3 cm.

Area of each blue triangle = ½ × 7 × 3

= ½ × 21

= 10.5 cm2

3 cm

This diagram shows a yellow square inside a blue square.

Area problems

7 cm

10 cm

We can work this out by subtracting the area of the four blue triangles from the area of the whole blue square.

There are four blue triangles so:

Area of four triangles = 4 × 10.5 = 42 cm2

Area of blue square = 10 × 10 = 100 cm2

Area of yellow square = 100 – 42 = 58 cm2

3 cm

This diagram shows a yellow square inside a blue square.

What is the area of the yellow square?

Area formulae of 2-D shapes

You should know the following formulae:

b

hArea of a triangle = bh

12



b

h

a

h

b

Using units in formulae

Remember, when using formulae we must make sure that all values are written in the same units.

For example, find the area of this trapezium.

76 cm

1.24 m

518 mm

Let’s write all the lengths in cm.

518 mm = 51.8 cm

1.24 m = 124 cm

Area of the trapezium = ½(76 + 124) × 51.8

= ½ × 200 × 51.8

= 5180 cm2

Don’t forget to put the units at the end.

WARM UP 12/2/15

Solve the following rebus puzzles

Surface Area

Rectangular PrismThe surface area S.A. of a rectangular prism with base l, width w, and height h is the sum of the areas of its faces.

S.A. = 2lh + 2lw + 2hw

Practice Problem 1 Find the surface area of the

rectangular prism shown to the right.

Triangular Prism• To find the surface area of a triangular

prism, it is more efficient to find the area of each face and calculate the sum of all of the faces.

Practice Problem 2• Find the surface area of the triangular prism shown to the right.• Find the area of each shape and add.

Area of rectangle 1 Area of rectangle 2 Area of rectangle 3Area of the triangles

WARM UP 12/3/15

How many faces are in the following pictures?

60

VOLUME

What is Volume?

Volume is the measure of the capacity of a container.

It is the measure of how much a container of a particular shape will hold - liquids, dry substances, etc.

Cubic Units Volume is measured in cubic units. Use cubes to fill a rectangular prism

such as a box.

One Cubic Unit

1 unit(height)

1 unit(length)

1 unit(width)

A unit might be measured in inches, feet,

centimeters, etc.

A unit might be measured in inches, feet,

centimeters, etc.

How many cubic units is this rectangle?

What did you find?

Yes, it is 8 cubic units!

How about this one?

Remember… there are

some cubes you can’t see!

Watch...

Now Count Them

What did you find?

Yes! There are 12 cubic

units!

What’s the formula?

The formula for finding the volume of a rectangle is ….

L x W x H = VolumeL x W x H = Volume

This means we take the This means we take the lengthlength times the times the width,width, then then multiply that by the multiply that by the heightheight..

Let’s try it!

L = 3

H = 3

W = 2

3 x 3 x 2 = 18 cubic units

Find the volume of this one!

What did you find?

4 x 2 x 3 = 24 cubic units

Volume and Surface Area

The volume V and surface area S of a cube with side lengths of s are given by the formulas:

V = s3

Volume and Surface Area of a Cube

s

ss

5 ft.

Find the volume and surface area of the cube below.

V = 53 S = 6(5)2

V = 125 ft.3 S = 625

S = 150 ft.2

and

S = 6s2


Volume is a measure of capacity of a space figure. It is always measured in cubic units.

Surface Area is the total region bound by two dimensions. It is always measured in square units.

w

h

l

The volume V and surface area S of a box with length l, width w, and height h is given by the formulas:

V = lwh

Volume and Surface Area of a Rectangular solid (box)

and

S = 2lw + 2lh + 2hw

9-476

2 in.

3 in.

7 in.

Find the volume and surface area of the box below.

V = 7(2)(3)

V = 42 in.3

S = 2(7)(2) + 2(7)(3) + 2(3)(2)

S = 28 + 42 + 12

S = 82 in.2

Volume and Surface Area Volume of a Pyramid

The volume V of a pyramid with height h and base of area B is given by the formula:

Find the volume of the pyramid (rectangular base) below.

cm3

Note: B represents the area of the base (l w).

7 cm

6 cm3 cm

WARM UP 12/4/15

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Circumference, Area of a Circle

Circles A circle is the set of all points in a plane

that are the same distance from a given point, called the center.

CirclesThe diameter (d) is the distance across a circle through the center of the circle.

The radius (r) is the distance from the center to any point on the circle.

The circumference (C) is the distance around a circle.

Circles Pi is a non-terminating and non-repeating

number represented by the Greek letter (pi) 3.14 is often used as an approximation for

.

Pi is number that is approximately equal to 3.14. It is the number you get if you divide the circumference of any circle by its diameter. It's the same for all circles. You can approximate pi for yourself by taking some circular things like the tops of jars and CD's and frisbees and measuring their diameter and their circumference. When you divide the circumference by the diameter, you'll get an answer something like 3.14. It will be the same every time (unless you measured wrong).

Use think link to learn more!https://www.youtube.com/watch?v=DLZMZ-CT7YU

Circles Formulas for finding Circumference C = d C = 2r If you are given the diameter in a problem

use the formula with d. If you are given a problem with the radius use the formula with r.

Both formulas find the circumference.

Find Circumference

21 in•Which formula for C will you use?

•C = 2r

•C = 2(21)

•C = 131.9 inches

Your TurnFind the Circumference

4.5cm

•Which formula for C will you use?

•C = d

•C = (4.5)

•C = 14.1cm

Circles - Area Formula for finding the area of a circle: A = r If you are given the diameter instead of

the radius; divide the diameter by 2 to get the radius.

2

Find the Area

14m

•D = 14 m r = ?

•14 ÷ 2 = 7 m

•A =r

•A =(7 )

•A = (49)

•A = 153.9 m

2

2

2

Your Turn Find the Area

5 ft

•A =r

•A =(5 )

•A = (25)

•A = 78.5 ft

2

2

2

Surface Area of a Cylinder The surface area S.A. of a cylinder with

height h and radius r is the area of the two bases plus the area of the curved surface (parallelogram).

Model Net Area

2 circular bases

2 congruent circles with radius r

1 curved surface

1 rectangle with width h and length

Practice Problem Find the surface area of the

cylinder. Round your answers to the nearest hundredth.

Volume of Surface Area of a Right Circular Cylinder

10 m2 m

The volume V and surface area S of a right circular cylinder with base radius r and height h are given by the formulas:


Find the volume and surface area of the cylinder below.

V = (2)2(10)

V = 40V = 125.6 m3

S = 2(2)(10) + 2(2)2

S = 40 + 8 = 48

S = 150.72 m2

V = r2hh

r

and

S = 2rh + 2r2

Volume of Surface Area of a Sphere

r

The volume V and surface area S of a sphere radius r are given by the formulas:


V = (4/3) r3

Find the volume and surface area of the sphere below.

9 in. S = 4 (9)2V = (4/3)(9)3

V = 972V = 3052.08 in.3

S = 324S = 1017.36 in.2

and

S = 4 r2


Volume of Surface Area of a Right Circular Cone

The volume V and surface area S of a right circular cone with base radius r and height h are given by the formulas:

Find the volume and surface area of the cone below.

V = (1/3)(3)2(4)

V = 12V = 37.68 m3

S = 15 + 9S = 24S = 75.36 m2

h = 4 m

r = 3 m

warm up 11/30/15 write down one fun thing that you did over thanksgiving weekend; turn to a neighbor...

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perimeter perimeter

perimeter of squareperimeter

given rectangle

given figure

rectangular shape

p cm4 p cm4 p cmnone

square garden

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