McGraw-Hill Education GRE 2019

Perimeter of a Triangle

The perimeter of a triangle is the sum of all the side lengths.

7

3 5

QS

R

The perimeter of the preceding triangle is 3 + 5 + 7 = 15.

Area of a Triangle

The area of a triangle refers to the amount of space within the triangle. Area is

expressed in square units, such as cm^2 (square centimeters), in.^2 (square inches),

and so on. The formula for the area of a triangle is (^12 ) × b × h.

Note that the base (b) and height (h) must be perpendicular to each other.

Look at the following figure:

7

8

A B

C

In this example, the base is 8 and the height is 7. You know that the height is 7

because the line segment drawn from angle C creates a perpendicular angle when it

intersects the base, AB. The area of this triangle will thus be^12 × 8 × 7 = 28.

In the example, AB was the base of the triangle. However, any side can be the

base of a triangle. The height will be defined as the perpendicular line from the

angle opposite the base. Next, you will see the same triangle as earlier, but now BC

is the base.

14 4

A B

C

Now, to calculate the area:^12 × 4 × 14 = 28.

Sometimes you will have to extend the base to determine the corresponding height:

6

3

B C

A

In this example, the base is 6. To draw the height, it was necessary to extend base

BC until it intersected the height. The area of this triangle is^12 × 6 × 3 = 9.

CHAPTER 13 ■ GEOMETRY 379

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