Trapezoid

A trapezoid (American English) or trapezium (British English) is a quadrilateral two of whose sides are parallel to each other. Note that there is another confusingly-named quadrilateral with no parallel sides: the trapezius (American English) or trapezoid (British English). To avoid confusion, this article uses the American English wording.

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If the other pair of opposite sides is also parallel, then the trapezoid is also a parallelogram.

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Otherwise, the other two opposite sides may be extended until they meet at a point, forming a triangle that the trapezoid lies inside.

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A quadrilateral is a trapezoid if and only if it contains two adjacent angles that add up to one straight angle, i.e., to 180 degrees or π radians. Another necessary and sufficient condition is that the diagonals cut each other in mutually the same ratio.

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The area of a trapezoid can be computed as the arithmetic mean of the lengths of the two parallel sides, multiplied by the distance along a perpendicular line between them. 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.

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Thus, if a and b are the two parallel sides and h is the distance (height) between the parallels, the area formula is as below:

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A=rac{1}{2}(a+b)h or A=rac{h(a+b)}{2}

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American English: American English (AmE) is the form of the English language used mostly in the United States of America. It is the primary language used in the United States. As of 2005, more than two-thirds of native speakers of English use various forms of American English. American English is also sometimes calle...

British English: British English (BrE) is a term used loosely to refer to the form of the English language written in the British Isles, and more narrowly as spoken in the south of England (extending elsewhere with varying degrees). For historical reasons dating back to the rise of London in the 9th century, the var...

Quadrilateral: Other uses: Quadrilateral (disambiguation)...