Trapezoid Calculator

The longer base a lies along the bottom from (0, 0) to (a, 0); the shorter base b sits at height h starting at an offset x from the left. With the height known the page centres the top base (x = (a − b)/2, an isosceles trapezoid) unless you give an offset — 0 makes the left leg vertical (a right trapezoid), and an offset outside 0…a − b overhangs. The legs are then the hypotenuses √(x² + h²) and √((a − b − x)² + h²). If the shorter base is typed first the two are swapped and a note says so.

With legs c and d and the difference e = a − b, the top base can be placed in exactly one way: x = (c² − d² + e²) ÷ 2e and h = √(c² − x²). If c² < x² the legs cannot reach across the difference — the triangle inequality |c − d| < e < c + d fails — and the page reports it. Equal bases with legs given are a parallelogram whose height is not determined, so the height must be entered instead.

Area = ½(a + b)·h, which is also the midsegment ½(a + b) — the average width — times the height. The four corner angles come from the dot product of the two edges at each corner, so they add to 360° and the two along each leg add to 180°; the diagonals are the distances between opposite corners. The type is named from the result: isosceles (equal legs), right (a vertical leg), scalene, or rectangle / parallelogram when the bases are equal (the inclusive definition). Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.