请输入您要查询的字词:

 

单词 Trapezoid
释义

trapezoid


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. (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 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.

..b1b2

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

A=12(b1+b2)h.

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

m=12(b1+b2).

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

A=mh.
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 17:21:15