How this instrument works
For a general trapezoid — one where the two non-parallel legs aren't assumed equal — recovering a missing leg from the other known measurements takes an extra step beyond the isosceles case. Dropping perpendiculars from both ends of the shorter base down to the longer one splits the total horizontal gap between the bases into two separate pieces, one under each leg. The known leg's own piece is found first via the Pythagorean theorem, offset₁ = √(leg₁² − height²), and whatever remains of the total gap, offset₂ = (b₂−b₁) − offset₁, belongs to the missing leg, which then follows from that same theorem applied again: leg₂ = √(offset₂² + height²).
This deliberately makes NO assumption that the two legs are equal, unlike this site's isosceles-trapezoid-specific pages, which rely on that symmetry to split the horizontal gap evenly between both sides. A general trapezoid's two legs can lean at completely different angles, and this calculator's two-step offset method handles that asymmetry correctly.
A useful sanity check: if the known leg's own offset already accounts for the entire horizontal gap between the bases, the missing leg's offset comes out to exactly zero, and that leg stands perfectly perpendicular — the boundary case where the trapezoid is actually a right trapezoid on that side.
- Enter the shorter parallel base into the Base 1 (shorter) field.
- Enter the longer parallel base into the Base 2 (longer) field.
- Enter the known leg's length into the Leg 1 (known) field.
- Enter the trapezoid's height into the Height field.
- Read Leg 2 (missing): the sheet works out both horizontal offsets and applies the Pythagorean theorem to recover it.
Worked example — bases 6 and 14, known leg 5, height 4
A general trapezoid has bases 6 and 14, a known leg of 5, and a height of 4. The known leg's own offset is √(25−16)=3, leaving (14−6)−3=5 for the missing leg's offset, and the missing leg is √(25+16)=√41≈6.40 — recovered without ever assuming the two legs match.
Bases 6 and 6 (equal) with a known leg of 3 and height 3 give a missing leg of exactly 3 too — with no horizontal gap to split at all between equal bases, both legs stand perfectly perpendicular, and the trapezoid is actually a rectangle.
Questions
How do you find a trapezoid's missing leg?
First find the known leg's own horizontal offset via the Pythagorean theorem, then subtract that from the total gap between the two bases to find the missing leg's offset, and apply the Pythagorean theorem once more to recover the missing leg's length.
Does this assume the trapezoid is isosceles?
No — this deliberately makes NO assumption that the two legs are equal, unlike this site's isosceles-trapezoid-specific pages. A general trapezoid's legs can lean at entirely different angles, and this two-step offset method handles that correctly.
What does a missing-leg offset of zero mean?
That leg stands perfectly perpendicular to the bases — the boundary case where the trapezoid is a right trapezoid on that particular side, with the known leg's own offset already accounting for the entire horizontal gap between the bases.
What if the known leg is shorter than the height?
No real trapezoid exists with those measurements — the leg is the hypotenuse of its own internal right triangle, and a hypotenuse can never be shorter than either of that triangle's legs, including the height.
What if the two bases are equal?
The trapezoid becomes a rectangle, and both legs stand perpendicular to the bases — the missing leg comes out equal to the known leg exactly, since there's no horizontal gap left to split between the two sides at all.