A trapezoid is a quadrilateral with two sides parallel. The trapezoid is equivalent to the British definition of trapezium (Bronshtein and Semendyayev 1977, p. 174). An isosceles trapezoid is a trapezoid in which the base angles are equal so . A right trapezoid is a trapezoid having two right angles.
The area of the trapezoid is
(1)
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(2)
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(3)
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where
(4)
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(5)
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and
(6)
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is the semiperimeter.
The geometric centroid lies on the median between the base and top, and if the lower left-hand corner of the trapezoid is at the original, lies at
(7)
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(8)
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(9)
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(cf. Harris and Stocker 1998, p. 83, who give but not ).
The trapezoid depicted has central median
(10)
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If vertical lines are extended from the endpoints of the upper side, the bases of the triangles formed on the left and right are
(11)
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(12)
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respectively. This gives the vertex angles as
(13)
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(14)
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(15)
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(16)
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from the lower left corner proceeding counterclockwise.
In terms of the side length, the diagonals of the trapezoid are given by
(17)
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(18)
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and the height by
(19)
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with as defined above.
Letting the lower left vertex be located at the origin, the intersection of the diagonals occurs at
(20)
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(21)
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The areas of the indicated triangles are
(22)
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(23)
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(24)
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(25)
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so
(26)
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and
(27)
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(B. Gladman, pers. comm., Apr. 20, 2006).