# Trapezoid

A trapezoid is a geometric figure that lies in a plane. It is also a type of quadrilateral.

## Definition

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.

## Terminology

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. A trapezoid is cyclic if and only if it is isosceles.

The median of a trapezoid is defined as the line connecting the midpoints of the two legs. Its length is the arithmetic mean of that of the two bases $\dfrac{b_1+b_2}{2}$. It is also parallel to the two bases.

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.

## Related Formulas

If $A$ denotes the area of a trapezoid, $b_1,b_2$ are the two bases, and the perpendicular height is $h$, we get $\[A=\dfrac{h}{2}(b_1+b_2)\]$