Basic Mathematics for College Students

9.7 Perimeters and Areas of Polygons 783

EXAMPLE (^7) Find the area of the triangle shown on
the right.
StrategyWe will substitute 8 for and 5 for in the
formula and evaluate the right side. (The side
having length 6 cm is additional information that is not
used to find the area.)
WHYThe variable represents the unknown area of the triangle.
Solution
This is the formula for the area of a triangle.
Substitute 8 for b,the length of the base, and 5 for h,the height.
Do the first multiplication:.
Complete the multiplication.
The area of the triangle is 20 cm^2.

 20

1

4(5) 2 (8) 4

A

1

2

( 8 )( 5 )

A

1

2

bh

A

A^12 bh

b h

Self Check 7

Find the area of the triangle

shown below.

8 cm

6 cm

5 cm

15 mm

12 mm

17 mm

Now TryProblem 45

EXAMPLE (^8) Find the area of the triangle
shown on the right.
StrategyWe will substitute 9 for and 13 for
in the formula and evaluate the right
side. (The side having length 15 cm is additional
information that is not used to find the area.)
WHYThe variable represents the unknown
area of the triangle.
SolutionIn this case, the altitude falls outside the triangle.
This is the formula for the area of a triangle.
Substitute 9 for b,the length of the base, and 13 for h,the height.
Write 9 as and 13 as.
Multiply the fractions.
Do the division.
The area of the triangle is 58.5 cm^2.

58.5



117

2

13

1

9

 1

1

2

a

9

1

ba

13

1

b

A

1

2

( 9 )( 13 )

A

1

2

bh

A

A^12 bh

b h

Self Check 8

Find the area of the triangle

shown below.

7 ft

3 ft 4 ft

Now TryProblem 49

Self Check 9

Find the area of the trapezoid

shown below.

12 m

6 m

6 m

9 cm

15 cm

13 cm

EXAMPLE (^9) Find the area of the trapezoid shown
on the right.
StrategyWe will express the height of the trapezoid in
inches and then use the formula to find the
area of the figure.
WHYThe height of 1 foot must be expressed as 12 inches
to be consistent with the units of the bases.
A^12 h(b 1 b 2 )
6 in.
1 ft
10 in.
58.5
2  117.0
 10
17
 16
10
 10
0
1
2
3
 9
117