Basic Mathematics for College Students

The perimeter is 70 m.

 70

P 10  18  24  18

9.7 Perimeters and Areas of Polygons 777

SECTION 9.7

Perimeters and Areas of Polygons

In this section, we will discuss how to find perimeters and areas of polygons. Finding
perimeters is important when estimating the cost of fencing a yard or installing crown
molding in a room. Finding area is important when calculating the cost of carpeting,
painting a room, or fertilizing a lawn.

Objectives

1 Find the perimeter of a

polygon.

2 Find the area of a polygon.

3 Find the area of figures that are

combinations of polygons.

1 Find the perimeter of a polygon.

The perimeterof a polygon is the distance around it. To find the perimeter of a
polygon, we simply add the lengths of its sides.

P

Image Copyright iofoto, 2009. Used under license fromShutterstock.com

Triangle

7 ft

6 ft 8 ft

Quadrilateral

18 m 18 m

10 m

24 m

Pentagon

1.2 yd

3.4 yd

5.2 yd

6.6 yd

7.1 yd

The perimeter is 21 ft.

 21

P 6  7  8

The perimeter is 23.5 yd.

23.5

P1.27.16.65.23.4

For some polygons, such as a square and a rectangle, we can simplify the
computations by using a perimeter formula. Since a square has four sides of equal
length , its perimeter is s P ssss, or. 4 s

Perimeter of a Square

If a square has a side of length , its perimeter is given by the

formula

P 4 s

s P

ss

s

s

EXAMPLE (^1) Find the perimeter of a square whose sides are 7.5 meters
long.
StrategyWe will substitute 7.5 for in the formula and evaluate the right
side.
WHYThe variable represents the unknown perimeter of the square.
Solution
This is the formula for the perimeter of a square.
Substitute 7.5 for s,the length of one side of the square.
Do the multiplication.
The perimeter of the square is 30 meters.

P 30

P4(7.5)

P 4 s

P

s P 4 s

Self Check 1

A Scrabble game board has a

square shape with sides of length

38.5 cm. Find the perimeter of

the game board.

Now TryProblems 17 and 19

7

2

.5

 4

30.0