Solve for a trapezoid’s missing base when you already know its area, one base, and its height.
How it works
Rearranging the trapezoid area formula for the unknown base gives b₂ = (2 × area ÷ height) − b₁. An area of 50 with a known base of 8 and height of 5 means the missing base is 12.
What this does not include
This is the algebraic reverse of this site’s general trapezoid area calculator, which goes the opposite direction — from both bases and height to area — rather than solving for a missing base.
How to use this calculator
- Enter the trapezoid’s area.
- Enter the base you already know.
- Enter the height.
A worked example
Given an area of 50, base1 of 8, and height of 5: solving for base2 = (2×area/height) − base1 = (2×50/5) − 8 = 12.
Given area 40, base1 8, height 5: base2 = 8 — an equal-base trapezoid, which is really a rectangle in disguise.
What the variables mean
| Variable | Meaning |
|---|---|
| Area | Known trapezoid area |
| Base1 | Known length of one parallel side |
| Height | Perpendicular distance between the two parallel sides |
Edge cases worth knowing
This is the reverse of the standard trapezoid area calculation — solving for a missing base when the area, one base, and height are already known, rather than computing area from all four values. See this site’s area-of-a-trapezoid calculator for the forward direction.
An area too small for the given base1 and height produces a negative or invalid base2, so the calculator declines to show a result for a geometrically impossible combination.
When would you know a trapezoid’s area but not both bases?
A common case is working backward from a stated area (like a land plot or a cross-sectional area in an engineering drawing) to find a dimension that wasn’t directly measured or specified.
What if the calculated missing base comes out zero or negative?
That means the area, known base, and height combination isn’t physically possible for a trapezoid — this calculator returns no result rather than an invalid length.
Does it matter which base I enter as the “known” one?
No — the formula is symmetric, so entering either base as the known value and solving for the other works the same way.
