How this calculator works
The midsegment is the average of the two parallel bases. Multiplying it by perpendicular height gives area. The reverse formulas isolate either base or the height. The decomposition table splits the area into a rectangle as wide as the shorter base plus the combined triangular excess. Four-side mode solves the horizontal leg offset, then finds height with the Pythagorean theorem and reports the four interior angles.
Formula
K = (a+b)h/2; h = 2K/(a+b); a = 2K/h - b; offset = [(a-b)+(c²-d²)/(a-b)]/2.
Worked example
Bases 8 m and 4 m with height 3 m give area 18 m². The decomposition is 12 m² from the shorter-base rectangle and 6 m² from the excess triangles. If area is 18 m² and the other base is 4 m, reversing gives a = 8 m.
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Frequently asked questions
Which sides are the bases?
The bases are the parallel sides. Their names can be swapped without changing area.
Can I use the sloping leg as height?
Only if it is perpendicular to both bases. Otherwise use the true height or the four-side method.
Why can equal bases fail in four-side mode?
Equal bases leave the horizontal offset undetermined from these measurements. Supply a measured height; area mode accepts equal bases.