How this instrument works
An isosceles trapezoid has two equal, non-parallel legs, and this calculator uses that symmetry to find the height from measurements that don't include the height directly. Dropping a perpendicular from each end of the shorter base down to the longer one splits the horizontal gap between them evenly, into two pieces of (b₂−b₁)⁄2 each, and each of those pieces forms a right triangle with the leg as the hypotenuse — so the Pythagorean theorem gives height = √(leg² − ((b₂−b₁)⁄2)²) directly.
This is a genuinely different starting point from the general Trapezoid page elsewhere on this site, which takes the height as a direct known input. Here, only the two bases and one equal leg length are needed — often exactly what's actually measurable in the field (the parallel top and bottom, and one slanted side), with the height itself hidden and requiring this derivation to recover.
Once the height is found, the area follows the ordinary trapezoid formula, ½(b₁+b₂)×height — this calculator simply automates the intermediate step most trapezoid-area problems skip over silently.
- Enter the shorter parallel base into the Base 1 (shorter) field.
- Enter the longer parallel base into the Base 2 (longer) field.
- Enter the length of either equal leg into the Leg (both equal legs) field.
- Read Height and Area: the sheet derives the height via the Pythagorean theorem, then applies the standard trapezoid area formula.
Worked example — bases 6 and 10, legs of 5
An isosceles trapezoid has parallel bases of 6 and 10, with both equal legs at 5. The horizontal offset on each side is (10−6)⁄2 = 2, so the height is √(25−4) = √21 ≈ 4.58, and the area is ½(6+10)×4.58 ≈ 36.66 — the height recovered entirely from the bases and the leg, with no separate height measurement ever needed.
Equal bases of 6 and 6 turn the shape into a plain rectangle, and the height correctly comes out to exactly 5, matching the leg length itself — with no horizontal offset to account for, the leg stands perfectly perpendicular, and the area becomes simply 6×5=30.
Questions
How do you find an isosceles trapezoid's height from its bases and legs?
h = √(leg² − ((b₂−b₁)⁄2)²) — dropping a perpendicular from a short-base corner down to the long base creates a right triangle with the leg as hypotenuse and half the difference between the two bases as one leg of that triangle, letting the Pythagorean theorem recover the height.
How is this different from the general Trapezoid calculator?
The general page takes the height as a direct known input, alongside both bases and both legs. This page instead assumes the two legs are EQUAL (a genuinely isosceles trapezoid) and derives the height itself from just the bases and one leg length, when the height isn't already known.
What if the leg is too short for the given bases?
The value under the square root, leg² − ((b₂−b₁)⁄2)², would come out negative — geometrically impossible, since the leg would be too short to reach across the required horizontal gap. This calculator flags that combination as invalid.
What happens if the two bases are equal?
The trapezoid becomes a rectangle, and the derived height simply equals the leg length itself, since there's no horizontal offset left for the leg to angle across — the leg stands perfectly perpendicular to both bases.
Why must the two legs be equal for this formula to work?
The formula relies on the horizontal offset splitting EVENLY between the two sides, which is only guaranteed when the trapezoid is genuinely isosceles. A general trapezoid with two different leg lengths would need a different, more involved derivation to recover its height this way.