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.

Related Topics:
American English - British English - Quadrilateral - Parallel

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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.

Related Topics:
If and only if - Angle - Degree - π - Radian - Diagonal - 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.

Related Topics:
Area - Arithmetic mean - Perpendicular

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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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