How this calculator works
Subtracting three known boundary lengths from the perimeter gives the fourth. A positive answer alone is insufficient: the two bases must be unequal and their difference must fit strictly between the difference and the sum of the legs. These inequalities ensure that the legs can span the bases at a positive height. The height readout gives a second geometric check on the recovered side. Either base may be the longer one.
Formula
Missing side = P - sum of three known sides. With Δ = |a-b|, a non-flat trapezoid requires |c-d| < Δ < c+d. Height follows from x = (Δ²+c²-d²)/(2Δ), h² = c²-x².
Worked example
Perimeter 24 m, base b = 4 m and legs c = d = 5 m leave base a = 24-4-5-5 = 10 m. The base difference is 6 m, each leg has horizontal projection 3 m and the height is 4 m.
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Frequently asked questions
Can I find a missing leg instead of a base?
Yes. Select either leg and enter both bases, the other leg and the perimeter.
Why can a positive missing side be invalid?
The remaining measurements may not let the legs join the parallel bases. A flat outline or an impossible span is rejected.
What happens if the bases become equal?
That gives a parallelogram case whose height is not determined by its sides. This tool requires unequal bases so its height check has a unique result.