A trapezoid is a quadrilateral 'only' two of whose sides are parallel to each other. (In some european countries and Korea, a trapezoid is defined as a quadrilateral mindestens two of whose sides are parallel to each other. By this definition, parallelogram is also a trapezoid.)
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. (But according to some authorities, parallelograms are specifically excluded from the definition of trapezoid.) 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 radian.
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.
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.
