A Guide to the GRE/Trapezoids

Rules
The area of a trapezoid equals the average of the bases divided by the height.

The area equalsor 72.

When not given, the height of a trapezoid can often be deduced using the Pythagorean Theorem

In this figure, we split the trapezoid into a right triangle with a leg of 3 (10 - 5 -2) as seen to the right. The height of the triangle is 52 minus 32, which is equal to 4.

Practice
1. If the trapezoid below has an area of 22, what is the length of its top side?

2. What is the area of the trapezoid above?

Answers to Practice Questions
1. 4

The area of a trapezoid equals the average of its bases multiplied by its height. Since the height of this trapezoid is 4, the average of its bases must equal 22 divided by 4, or 5.5. At this point, the top side can be determine by solving the equation= 5.5, which works out to 4.

2. 192

This trapezoid can be split into a right triangle with sides of 20 and 16, the latter determined by subtracting 8 from 24. This means that the height of the trapezoid is the third side of the right triangle, which equals or 12. 12 multiplied by the average of the bases - 16 - equals 192.