How this calculator works
Area divided by the average base length gives height. The leg-angle method drops a perpendicular between the bases, resolving the leg into vertical and horizontal components. Sine gives the positive vertical height for any interior angle between zero and 180 degrees. Cosine gives a signed projection: negative values identify a leg leaning outward relative to the chosen base direction. A single leg and angle determine height without fixing both base lengths.
Formula
m = (a+b)/2; h = K/m = 2K/(a+b). From leg c and interior angle α: h = c sin α; horizontal projection = c cos α.
Worked example
Bases 8 m and 4 m have average length 6 m. An area of 18 m² therefore gives height 3 m. Alternatively, a 10 m leg at 150° gives height 5 m and projection approximately -8.6603 m.
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Frequently asked questions
Can I use an obtuse angle?
Yes. Its sine is positive, while its cosine makes the horizontal projection negative.
Does the leg equal the height?
Only when it is perpendicular to the bases, so its interior angle is 90 degrees.
Can these inputs determine perimeter?
Area and the bases do not determine both legs. One leg and angle likewise do not determine the complete trapezoid, so perimeter is omitted.