Isosceles Trapezoid
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
TrapezoidExplore with Wolfram|Alpha
WolframAlpha
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.Referenced on Wolfram|Alpha
Isosceles TrapezoidCite this as:
Weisstein, Eric W. "Isosceles Trapezoid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IsoscelesTrapezoid.html