Basic Mathematics for College Students

9.7 Perimeters and Areas of Polygons 781

Figure Name Formula for Area

Square , where is the length of one side.

Rectangle , where is the length and is the width.

Parallelogram , where is the length of the base and is the height.

(A height is always perpendicular to the base.)

Triangle , where is the length of the base and is the height.

The segment perpendicular to the base and representing the

height (shown here using a dashed line) is called an altitude.

Trapezoid , where is the height of the trapezoid and

b 1 and b 2 represent the lengths of the bases.

A^12 h(b 1 b 2 ) h

h

b 1

b 2

A^12 bh b h

h

b

h

b

Abh b h

h

b

Alw l w

ww

l

l

As^2 s

ss

s

s

EXAMPLE (^4) Find the area of the square shown on
the right.
StrategyWe will substitute 15 for in the formula
and evaluate the right side.
WHYThe variable represents the unknown area of the square.
Solution
This is the formula for the area of a square.
Substitute 15 for s,the length of one side of the square.
Evaluate the exponential expression.
Recall that area is measured in square units. Thus, the area of the square is
225 square centimeters, which can be written as 225 cm^2.

A 225

A 152

As^2

A

s As^2

Self Check 4

Find the area of the square

shown below.

20 in.

20 in.

20 in. 20 in.

Now TryProblems 29 and 31

EXAMPLE (^5) Find the number of square feet in 1 square yard.
StrategyA figure is helpful to solve this problem. We will draw a square yard and
divide each of its sides into 3 equally long parts.
WHYSince a square yard is a square with each side measuring 1 yard, each side
also measures 3 feet.
Self Check 5
Find the number of square
centimeters in 1 square meter.
Now TryProblems 33 and 39
15 cm
15 cm
15 cm 15 cm
15
 15
75
150
225