# trapezoid

In some dialects of English (e.g. (http://planetmath.org/Eg) 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 segment  that is perpendicular   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 $b_{1}$ and $b_{2}$ and a height drawn in blue.

If a trapezoid has bases of lengths $b_{1}$ and $b_{2}$ and a height of length $h$, then the area of the trapezoid is

 $A=\frac{1}{2}(b_{1}+b_{2})h.$

Note that the length $m$ of the median of a trapezoid is the arithmetic mean  of the lengths of its bases; i.e. (http://planetmath.org/Ie),

 $m=\frac{1}{2}(b_{1}+b_{2}).$

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

 $A=mh.$
Title trapezoid Trapezoid 2013-03-22 17:11:52 2013-03-22 17:11:52 Wkbj79 (1863) Wkbj79 (1863) 10 Wkbj79 (1863) Definition msc 51-00 trapezium base leg height median