Basic Mathematics for College Students

784 Chapter 9 An Introduction to Geometry

Now TryProblem 53 Solution

This is the formula for the area of a trapezoid.

Substitute 12 for h,the height; 10 for b 1 , the length of

the lower base; and 6 for b 2 , the length of the upper base.

Do the addition within the parentheses.

Do the first multiplication:.

Complete the multiplication.

The area of the trapezoid is 96 in^2.

 96

1

6(16) 2 (12) 6



1

2

(12)(16)

A

1

2

( 12 )( 10  6 )

A

1

2

h(b 1 b 2 )

EXAMPLE (^10) The area of the parallelogram
shown on the right is 360 ft^2. Find the height.
StrategyTo find the height of the parallelogram,
we will substitute the given values in the formula
and solve for.
WHYThe variable represents the unknown height.
SolutionFrom the figure, we see that the length of the base of the parallelogram is
This is the formula for the area of a parallelogram.
Substitute 360 for A,the area, and 30 for b,the length of the base.
To isolate h,undo the multiplication by 30 by dividing both
sides by 30.
Do the division.
The height of the parallelogram is 12 feet.
12 h

360

30



30 h

30

360  30 h

Abh

5 feet25 feet30 feet

h

Abh h

Self Check 10

The area of the parallelogram

below is 96 cm^2. Find its height.

h

6 cm 6 cm

Now TryProblem 57

Self Check 11

Find the area of the shaded

figure below.

9 yd

3 yd

8 yd

5 yd

Now TryProblem 65

5 ft 25 ft

h

3 Find the area of figures that are combinations of polygons.

EXAMPLE (^11) Find the area of one side of the tent shown below.
Success Tip To find the area of an irregular shape, break up the shape into
familiar polygons. Find the area of each polygon and then add the results.
30 ft
12 ft
8 ft
20 ft
StrategyWe will use the formula to find the area of the lower
portion of the tent and the formula to find the area of the upper portion
of the tent. Then we will combine the results.
WHYA side of the tent is a combination of a trapezoid and a triangle.
A^12 bh
A^12 h(b 1 b 2 )
12
30  360
 30
60
60
0
1
3
6
 6
96