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Isosceles Trapezoid

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IsoscelesTrapezoid

An isosceles trapezoid (called an isosceles trapezium by the British; Bronshtein and Semendyayev 1997, p. 174) is trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal.

From the Pythagorean theorem,

h=sqrt(c^2-1/4(b-a)^2),
(1)

so

A=1/2(a+b)h
(2)
=1/2(a+b)sqrt(c^2-1/4(b-a)^2).
(3)

An isosceles trapezoid has perimeter

p=a+b+2c
(4)

and diagonal lengths

p=q=sqrt(ab+c^2).
(5)

See also

Trapezoid

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References

Bronshtein, I. N. and Semendyayev, K. A. Handbook of Mathematics, 3rd ed. New York: Springer-Verlag, 1997.Harris, J. W. and Stocker, H. Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 83, 1998.

Cite this as:

Weisstein, Eric W. "Isosceles Trapezoid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IsoscelesTrapezoid.html

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