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

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

(cf. Harris and Stocker 1998, p. 83, who give but not ).

The trapezoid depicted has central median

(7)

If vertical lines are extended from the endpoints of the upper side, the bases of the triangles formed on the left and right are

respectively. This gives the vertex angles as

from the lower left corner proceeding counterclockwise.

In terms of the side length, the diagonals of the trapezoid are given by

and the height by

(16)

where

where

(19)

is the semiperimeter .

Letting the lower left vertex be located at the origin, the intersection of the diagonals occurs at

The areas of the indicated triangles are

so

(26)

and

(27)

(B. Gladman, pers. comm., Apr. 20, 2006).

See also Isosceles Trapezoid ,

Parallelogram ,

Pyramidal Frustum ,

Rectangle ,

Right Trapezoid ,

Strombus ,

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References Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 123,
1987. Bronshtein, I. N. and Semendyayev, K. A. Handbook
of Mathematics, 3rd ed. New York: Springer-Verlag, 1997. Harris,
J. W. and Stocker, H. "Trapezoid." §3.6.2 in Handbook
of Mathematics and Computational Science. New York: Springer-Verlag, pp. 82-83,
1998. Kern, W. F. and Bland, J. R. Solid
Mensuration with Proofs, 2nd ed. New York: Wiley, p. 3, 1948.
Cite this as:
Weisstein, Eric W. "Trapezoid." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Trapezoid.html

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