Perimeter

The perimeter of a polygon isthe sum of the lengths of the sidesExample 1: Find the perimeter of ABC

O

A(-1,-2) B(5,-2)

C(5,6) AB = 5 – (-1) = 6BC = 6 – (-2) = 8

AC = 22 ))2(6())1(5(

= 1010086 22 AB + BC + AC = 6 + 8 + 10 = 24

Area of Squares and Rectangles

The area of a square is the length of the sides squared.

A = s2

The area of a rectangle is the product of its base and height.

A = bhb

h

s

s

Area of Parallelograms

The area of a parallelogram is the product of any base and its corresponding height.

A = bh

•Any side can be a base

h

b

•An altitude is a segment to the base drawn to the opposite base

•The height is the length of the altitude

Example 2

In parallelogram ABCD, DE and CF are altitudes. Find CF.

A E B10

FCD

1213

A = bh = 10(12) = 120A = bh = 13(CF) = 120

CF = 120/13 9.2 units2

Area of Triangles

The area of a triangle is half the product of any base and the corresponding height

h

b

A = bh2

1

Example 3

Find the area of the Triangle

8

7

A = ½ bh

A = (½) (7) (8) = 28 units2

Try it when b = 15 and h = 12

A = ½ bh = (½) (15) (12) = 90 units2

Area of 45-45-90 Triangles

The area of a 45-45-90 right triangle is one half of its leg length squared.

A = ½ s2

s

s

s2

45°

45°

Example 4

352

65

2

65s

A =

2

75

2

)3(25

2

35

2

35222

Find the area of the 45-45-90 right triangle.

56 cm

45°

45°265 shypotenuse

= 37.5 cm2

Area of 30-60-90 Triangles

The area of a 30-60-90 right triangle is:

2s

s

s3

30°

60°A = 2

2

3s

Example 5

Find the area of the 30-60-90 right triangle. Leave your answer in simple radical form.

4 in

30°

60° A = 2

2

3s

= in2 38)16(2

34

2

3 2

Area of Trapezoids

b2

b1

h

The area of a Trapezoid is half the product of the height and the sum of the two bases.

A = )(2

121 bbh

Example 6

h = 32

5mFind the area of trapezoid DUCK.

5m

h60°

D U

CK

2mA = )(

2

121 bbh

= )75)(32(2

1

= 312