Area—number of square units enclosed

Dimensions must all be the same unit

Altitude/Height—line perpendicular to the base with triangles, parallelograms, or trapezoids

Square/Rectangle

Perimeter (distance around)P = 4 x S (square)P = 2 L + 2 WAreaA = L x W (rectangle)A = S x S (square)

Circles (1/2 diameter)

Area

Radius

A = ∏ r ² or ∏ x r x r

Diameter

CircumferenceC = ∏ x d

ParallelogramA = b x h

TriangleA = ½ b x h

TrapezoidA = ½ h(b1 + b2)

*or you can treat the trapezoid like a composite figure by dividing it into simpler figure and finding the area then adding the totals

CirclesArea -- A = ∏r²Circumference -- C = ∏d

or 2r∏

3-D figures are also called space figures or solids

Vertex-where lines meet at a point Base-flat surface on the top and bottom

of the figure Base edge-lines along the base Lateral face-flat surface on sides of the

figure Lateral edge-lines along the sides of the

figure

Prism-2 parallel bases are congruent polygons and lateral faces are rectangles

sides are always rectangles

base (can be any shape; same on both ends)

Pyramid-1 polygon base the lateral faces are triangles vertex

sides are always triangles

base (can be any shape)

Cylinder-2 parallel bases that are congruent circles base (always a circle)

sides are rounded

Cone-1 circular base and 1 vertex vertex

base (always a circle)

Sphere-all points equal distance from center

Net—pattern you can form into a space figure

Named for the bases

You must know what shape the bases and faces form to be able to figure out a net

Cylinder Triangular Prism

Cube Rectangular Pyramid

Square Root– the inverse of squaring a number Symbol √ The square of an integer/number is a perfect

square On calculator: 2nd button then x² button then # then enter

Irrational Number—decimal form of a number that neither terminates or repeats If an integer isn’t a perfect square, its square root

is irrational

The first 13 perfect squares are easy to memorize:0² = 0 6² = 361² = 1 7²= 492² = 4 8² = 643² = 9 9² = 814² = 16 10²= 1005² = 25 11² = 1216² = 36 12²= 144* a square is a number times itself

Practice : (simplify & state whether it is rational or irrational)

1.) √642.) √1003.) - √164.) - √1215.) √276.) - √727.) - √508.) √2

Volume—number of cubic units needed to fill in a 3-D figure

Cubic unit—space occupied by a cube This is why the units are cubed

Rectangular Prism or CubeV = L x w x h

CylinderV = ∏r2 x h

Volume of Triangular V = (1/2 b x h) x h Prism Or V = b x h x h

Volume of a Cone or Pyramid 2Pyramid

V = 1/3 ( L x w) x h Or V = l x w x h

3

ConeV = 1/3 (∏ r2) x hOr V = ∏r² x h 3

Surface Area (S.A.)—sum of the area of the bases and the lateral sides of a space figure

Draw the figure Fill in all of the numbers for the edges Find area of each face and add everything

together Sometimes it helps to draw a net figure then

fill in the numbers

Find each of the following areas:

L x w L x h w x hThen add up all areas and multiply answer by 2

S.A. = l x w =

6 l x h = w x h = 5

sum = ? x 2 7 answer

= ?

*find area of circle then find area of rectangle add

*formula for area of rectangle is (∏d x h)

Area of the circle: A = ∏ r2

Ex: A = h= 11.5 cm A = ?

X 2

Area of the rectangle : A = ∏ x d x h A =

R = 3.5 cm A = ?

Total Area = ?

*

EX:

Area of Triangle: A = ½ b x h A = ½ (6 x 4) A = ? X 2

5 cm

6 cm 5 cm Area of Rectangle: A = l x w 6 cm 12cm A = 12 x 54 cm A = ? X 3

* There are 3 rectangle so multiply that area by 3

* There are 2 triangles so multiply that area by 2

Total Area = ?

Ex:

Area of Rectangle: A = l x w

A = 12 x 12A = ?

12 m 16 m Area of the Triangle: A = ½ b x

h 12 m A = ½ (12

x 16) A = ?

There are 4 triangles so multiply the area of the triangle by 4.Then add the area of the rectangle to the areas of the triangles.

Total Area = ?

Ex: Area of the Triangle: A = ½ b x h

A = ½ (8 x 10)

10 m A = ?

14 cm Area of the Circle: A = ∏ r2

A = 3.14 x 72

A = ?Add the areas of the circle and the triangle.

Total Area: ?

Ex:S.A. = 4∏ r2

d = 5 in

S.A. = 4 x 3.14 x 2.52

S.A. = ?