# 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. Notice that under this definition, every parallelogram is also a trapezoid. (Careful: some authors insist that a trapezoid must have exactly one pair of parallel sides.)

## 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 that is not a parallelogram, 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 $\[A=\dfrac{h}{2}(b_1+b_2)\]$