# Trapezoid

A **trapezoid** (American English) or **trapezium** (British English) is a quadrilateral two of whose sides are parallel to each other.

It is necessary that the two parallel sides be opposite; they cannot logically be adjacent.
If the other pair of opposite sides is *also* parallel, then the trapezoid is a parallelogram.
Otherwise, the other two opposite sides may be extended until they meet at a point, forming a triangle that the trapezoid lies inside of.

A quadrilateral is a trapezoid if and only if it contains two adjacent angles that add up to two right angles, i.e., to 180 degrees or &pi radians.

The area of a trapezoid can be computed as the product of the distance of the two parallel sides and the average (arithmetic mean) of the other two sides. This yields the well-known formula for the area of a triangle, were one to consider a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point.

Note that a trapezium (American English) or trapezoid (British English) does not have two parallel sides.

In acrobatics, the *trapeze* is a certain acrobatic device that is shaped like a trapezoid.

In anatomy, the *trapezoid bone* is a certain bone in the hand.