How this calculator works
A shear preserves area, giving the base-height rule. Side-angle mode projects side a onto the perpendicular direction. Diagonal mode uses four triangles around their intersection. Reverse angle mode reports the acute angle and its supplement; both have the same sine.
Formula
K = bh = ab sin θ = de sin φ / 2. b = K/h; h = K/b; b = K/(a sin θ); d = 2K/(e sin φ). θ = arcsin(K/(ab)) or π - θ.
Worked example
Sides 5 m and 8 m meeting at 30° have height 2.5 m and area 20 m². The same sides meeting at 150° also enclose 20 m². Diagonals 10 m and 6 m crossing at 90° enclose 30 m².
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Frequently asked questions
Can a sloping side be the height?
Only when it is perpendicular to the chosen base. Otherwise use side-angle mode.
Which diagonal angle should I enter?
Either of the two crossing angles gives the same area because their sines are equal.
Can area determine the shape?
Area alone cannot. Even with two fixed sides, supplementary included angles give the same area.