Basic Mathematics for College Students

782 Chapter 9 An Introduction to Geometry

Solution

Substitute 3 feet for 1 yard.

There are 9 square feet in 1 square yard.

9 ft^2

(3 ft)(3 ft)

(3 ft)^2

1 yd^2 (1 yd)^2 3 ft

3 ft

1 yd

1 yd

EXAMPLE (^6) Women’s Sports
Field hockey is a team sport in which
players use sticks to try to hit a ball into
their opponents’ goal. Find the area of
the rectangular field shown on the right.
Give the answer in square feet.
StrategyWe will substitute 100 for
and 60 for in the formula and
evaluate the right side.
WHYThe variable represents the unknown area of the rectangle.
Solution
This is the formula for the area of a rectangle.
Substitute 100 for l,the length, and 60 for w,the width.
Do the multiplication.
The area of the rectangle is 6,000 square yards. Since there are 9 square feet per
square yard, we can convert this number to square feet by multiplying 6,000 square
yards by.
Multiply by the unit conversion factor: 1.
Remove the common units of square yards in the
numerator and denominator. The units of ft^2 remain.
Multiply: 6,000  9 54,000.
The area of the field is 54,000 ft^2.
54,000 ft^2
6,0009 ft^2
9 ft^2
6,000 yd 1 yd 2
(^2) 6,000 yd (^2) 9 ft
2
1 yd^2
9 ft
2
1 yd^2

6,000

A 100 ( 60 )

Alw

A

w Alw

l

Self Check 6

PING-PONGA regulation-size

Ping-Pong table is 9 feet long

and 5 feet wide. Find its area

in square inches.

Now TryProblem 41

Striking

circle

Sideline

Centerline

Goal

cage

100 yd

Penalty 60 yd

spot

“The United States has more than 4,000 colleges and universities, with 2.3 million

students living in college dorms.”

The New York Times, 2007

The average dormitory room in a residence hall has about 180 square feet of

floor space. The rooms are usually furnished with the following items having

the given dimensions:

• 2 extra-long twin beds (each is 39 in. wide 80 in. long 24 in. high)


• 2 dressers (each is 18 in. wide 36 in. long 48 in. high)


• 2 bookcases (each is 12 in. wide 24 in. long 40 in. high)


• 2 desks (each is 24 in. wide 48 in. long 28 in. high)
  How many square feet of floor space are left?

THINK IT THROUGH Dorm Rooms