A trapezoidMathworldPlanetmath is a quadrilateralMathworldPlanetmath with at least one pair of sides parallelMathworldPlanetmathPlanetmath. Some insist that trapezoids have exactly one pair of sides parallel, in which case parallelogramsMathworldPlanetmath are not trapezoids. Other sources do not restrict the definition in this manner, in which case parallelograms are trapezoids. The convention in PlanetMath is to use the unrestricted definition.

In some dialects of English (e.g. ( British English), a trapezoid is referred to as a trapezium. Unfortunately, some confusion arises when this word is used, since in other dialects of English (e.g. American English), a trapezium is a quadrilateral without any parallel sides.

Below is a picture of a trapezoid.

The bases of a trapezoid are its two parallel sides. (If the trapezoid is a parallelogram, either pair of parallel sides can be declared to be its bases.) The legs of a trapezoid are the two sides that are not bases. A height of a trapezoid is a line segmentMathworldPlanetmath that is perpendicularPlanetmathPlanetmathPlanetmath to the bases of the trapezoid and whose endpoints lie on the two lines formed by extending the two bases. Typically, heights are drawn so that they intersect at least one base of the trapezoid. (For some trapezoids, it is impossible to draw a height that intersects both bases.) Below is a picture of a trapezoid with its bases labelled b1 and b2 and a height drawn in blue.


The median of a trapezoid is the line segment whose endpoints are the midpointsMathworldPlanetmathPlanetmathPlanetmath of the legs of the trapezoid. Below is a picture of a trapezoid with its median drawn in red.

In the of this entry, only Euclidean geometryMathworldPlanetmath is considered.

If a trapezoid has bases of lengths b1 and b2 and a height of length h, then the area of the trapezoid is


Note that the length m of the median of a trapezoid is the arithmetic meanMathworldPlanetmath of the lengths of its bases; i.e. (,


Thus, the area of a trapezoid can also be determined by

Title trapezoid
Canonical name Trapezoid
Date of creation 2013-03-22 17:11:52
Last modified on 2013-03-22 17:11:52
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 10
Author Wkbj79 (1863)
Entry type Definition
Classification msc 51-00
Defines trapezium
Defines base
Defines leg
Defines height
Defines median