Trapezoid

This is an AoPSWiki Word of the Week for Oct 18-24

A trapezoid is a geometric figure that lies in a plane. Trapezoids are characterized by having one pair of parallel sides. In general it is probably safe to assume that "one pair" means "exactly one pair," so that parallelograms are not also trapezoids. However, it is not clear that this is a universal mathematical convention.

The two parallel sides of the trapezoid are referred to as the bases of the trapezoid; the other two sides are called the legs. If the two legs of a trapezoid have equal length, we say it is an isosceles trapezoid. All isosceles trapezoids are cyclic.

Given any triangle, a trapezoid can be formed by cutting the triangle with a cut parallel to one of the sides. Similarly, given a trapezoid, one can reconstruct the triangle from which it was cut by extending the legs until they meet.

The area of the trapezoid is equal to the average of the bases times the height.

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