Basic Mathematics for College Students

9.7 Perimeters and Areas of Polygons 785

SolutionTo find the area of the lower portion of the tent, we proceed as follows.

This is the formula for the area of a trapezoid.

Substitute 30 for b 1 , 20 for b 2 , and 12 for h.

Do the addition within the parentheses.

Do the first multiplication:.

Complete the multiplication.

The area of the trapezoid is 300 ft^2.
To find the area of the upper portion of the tent, we proceed as follows.

This is the formula for the area of a triangle.

Substitute 20 for band 8 for h.

Do the multiplications, working from left to right:

and then.

The area of the triangle is 80 ft^2.
To find the total area of one side of the tent, we add:

The total area of one side of the tent is 380 ft^2.

380 ft^2

Atotal300 ft^2 80 ft^2

AtotalAtrap.Atriangle

21 (20) 10 10(8) 80

 80

Atriangle

1

2

( 20 )( 8 )

Atriangle

1

2

bh

 300

1

6(50) 2 (12) 6



1

2

(12)(50)

Atrap.

1

2

( 12 )( 30  20 )

Atrap.

1

2

h(b 1 b 2 )

EXAMPLE (^12) Find the
area of the shaded region shown
on the right.
StrategyWe will subtract the
unwanted area of the square
from the area of the rectangle.
Self Check 12
Find the area of the shaded
region shown below.
4 ft
4 ft
15 ft
9 ft
Now TryProblem 69
5 ft
5 ft
15 ft
8 ft
Area of shaded region = Area of rectangle – Area of square
WHYThe area of the rectangular-shaped shaded figure does not include the
square region inside of it.
Solution
The formula for the area of a rectangle is Alw.
The formula for the area of a square is As^2.
Substitute 15 for the length land 8 for the
width wof the rectangle. Substitute 5 for
the length sof a side of the square.
The area of the shaded region is 95 ft^2.

 95

 120  25

Ashaded 15 ( 8 ) 52

Ashadedlws^2

11

12

1

0

10

 25

95

1

4

5

 8

120