A **trapezoid** (or trapezoid) is a quadrilateral with exactly one pair* of parallel sides. In the figure below, *ABCD* is a trapezoid and *AB* is parallel to *CD*.

In this post, we derive the area of a trapezoid. We use the fact that a trapezoid can be partitioned into two triangles and one rectangle. The area of a trapezoid is equal to the sum of the areas of the two triangles and the area of the rectangle.

Observe that , , and .

We know that

**area of trapezoid = area of triangle 1 + area of rectangle + area of triangle 2.**

which means that .

Substituting the values we have

.

Simplifying the equation, rearranging the terms, and factoring result to

.

If we let the longer base of the trapezoid be , then, . Substituting we have

.

Therefore the area of a trapezoid with base and and altitude is

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*Other books define trapezoid as a quadrilateral with at least 1 pair of parallel sides.