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# Trapezoid

A trapezoid is a four-sided, two-dimensional polygon.

With four sides, a trapezoid is a quadrilateral, just as a square or rectangle or parallelogram. Unlike those forms, however, a trapezoid does not necessarily have to have parallel sides. In other words, all rectangles are trapezoids, but not all trapezoids are rectangles.

A trapezium is a subset of trapezoids in which at least two sides are parallel; a parallelogram is one example of a trapezium. The most common image of a trapezium, often confused with a trapezoid, is a figure with two parallel faces, one longer than the other. The two parallel sides of the trapezium are called the base lines, with the longer of the two called the base. If the two non-parallel sides are the same length, the trapezium is known as an isosceles trapezium.

One important mathematical use of the trapezoid is in the discipline of calculus. At its most fundamental, calculus can be used to determine the area under a curve. We can approximate this area by a series of trapezia—one side along the x-axis, two sides rising parallel to the y-axis, and the final side slanted to approximate the slope of the curve. As the trapezia get more and more narrow, the approximation grows more accurate. The calculus integral assumes that the trapezia have become increasingly narrow so as to yield the exact area under the curve.

Kristin Lewotsky

Figure 1. Illustration by Hans & Cassidy. Courtesy of Gale Group.

## KEY TERMS

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Parallelogram

—A quadrilateral in which opposite sides are parallel.

Trapezium

—A trapezoid in which two opposite sides are parallel.