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