Basic Mathematics for College Students

Area of a Triangle

The area Aof a triangle is one-half the product of its base band its height h.

The Language of MathematicsThe formula can be written

more simply as. The formula for the area of a triangle can also be

written as A

bh

2

.

A

1

2

bh

A

1

2

bh

Area

1

2

( base )( height ) or A

1

2

bh

3.2 Multiplying Fractions 227

EXAMPLE (^8) Geography Approximate the area of the state of Virginia
(in square miles) using the triangle shown below.
StrategyWe will find the product of 405, and 200.
WHYThe formula for the area of a triangle is A (base)(height).
Solution
This is the formula for the area of a triangle.
means. Substitute 405 for band 200 for h.
Write 405 and 200 as fractions.
In the numerator, multiply: 405  100 40,500.
The area of the state of Virginia is approximately 40,500 square miles. This can
be written as 40,500 mi^2.

 40,500

Factor 200 as 2 100. Then remove the common

factor of 2 from the numerator and denominator.



1  405  2

1

 100

2

1

 1  1

Multiply the numerators.

 (^) Multiply the denominators.

1  405  200

2  1  1



1

2



405

1



200

1

1

2 bh

1

 2 bh

1

2

 405  200

A

1

2

bh

200 mi

405 mi

Richmond

1

2

1

2 ,

Self Check 8

Find the area of the triangle

shown below.

Now TryProblems 49 and 99

16 in.

27 in.

Caution! Remember that area is measured in square units, such as in.^2 ,ft^2 ,

and cm^2. Don’t forget to write the units in your answer when finding the area

of a figure.

1. a. b. 2. 3. 4. 5. 6. a. b. c.
   7.64 votes 8.216 in.^2



9

16

9

16

8

125

3

26

2

5

7

3



5

18

10

27

1

16

ANSWERS TO SELF CHECKS

Virginia