Area of Trapezoid

Area of Trapezoid

A trapezoid (sometimes called a “trapezium” outside North America, but always a “trapezoid” on the GMAT, which uses American English), has one pair of parallel sides. The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides.


ScreenHunter_184 Oct. 13 16.45A trapezoid with bases of length a and b and a height of h

On the GMAT, you don’t have to do much with trapezoids. If you see one, you will most likely be asked to compute or make use of its area.

The area A of a trapezoid is:

where a and b are the lengths of the parallel sides, and h is the height.

The height is the perpendicular distance between the bases, whether or not that line happens to be vertical in your field of vision. So, for example, if the trapezoid above were rotated so that the line AD were at the bottom of the figure, the sides DC and AB would still be the bases of the trapezoid, since they are the parallel sides, and the dotted line labeled h would still be the height of the trapezoid, since it’s the distance between the bases.

You can think of the area of the trapezoid as the height times the average of the two bases, since that average is half the sum of the bases.

Practice Question

Trapezoid and circle:
http://www.gmatfree.com/trapezoid-and-circle
(you may want to review circles before trying this question)

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