Find an isosceles trapezoid’s height, area, and diagonal from its two parallel sides and the length of its equal (non-parallel) legs.
How it works
The height comes from a right triangle formed by the leg and half the difference of the two bases: height = √(leg² – ((b₁-b₂)/2)²). Area follows the usual trapezoid formula, and the diagonal uses the identity diagonal = √(leg² + b₁×b₂), specific to isosceles trapezoids. Bases of 12 and 8 with legs of 5 give a height of about 4.58, area of about 45.83, and diagonal of exactly 11.
What this does not include
This is distinct from this site’s general trapezoid area calculator, which takes height as a direct input for any trapezoid shape — this page instead derives height from the leg length, specific to the symmetric isosceles case.
How to use this calculator
- Enter the longer base.
- Enter the shorter base.
- Enter the leg (equal side) length.
Why must the legs be longer than half the base difference?
The leg forms the hypotenuse of a right triangle whose other leg is half the offset between the two bases — if the trapezoid’s legs were shorter than that offset, no valid triangle (and so no valid trapezoid) could exist.
Why does the diagonal formula not need the height directly?
It’s a special algebraic identity that holds specifically for isosceles trapezoids, letting the diagonal be found straight from the leg length and the two base lengths without computing height as an intermediate step.
Are both diagonals of an isosceles trapezoid equal?
Yes — that symmetry is one of the defining properties of an isosceles trapezoid, unlike a general trapezoid where the two diagonals can differ in length.
