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.) A trapezium (American English) or trapezoid (British English) has no parallel sides. Note that the meanings of both words are switched in the two variants of English.
If the other pair of opposite sides is also parallel, then the trapezoid (American English) is also 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 (American English) if and only if it contains two adjacent angles that add up to one straight angle, i.e., to 180 degrees or π radians. Another necessary and sufficient condition is that the diagonals cut each other in mutually the same ratio.
The area of a trapezoid (American English) can be computed as the arithmetic mean of the lengths of the two parallel sides, multiplied by the distance along a perpendicular line between them. 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.
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.