Trapezoid
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 two or more 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 π 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.
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.
Referenced By
List of mathematical topics (S-U) | Quadrilateral
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