How this calculator works
The altitude from the apex bisects the base and the apex angle. When height and area are known, dividing area by height gives half the base immediately. That half-base and the height form a right triangle whose hypotenuse is an equal leg. The other modes find the same half-base from trigonometry or Pythagoras. A denotes a length on this page; it does not denote the angle opposite a side as it does in some triangle diagrams.
Formula
Half-base A/2=K/H; A=2K/H. With equal leg B and apex angle β: A=2B sin(β/2), H=B cos(β/2). With B and H: A=2√(B²-H²).
Worked example
Height H=4 m and area K=12 m² give A=2×12/4=6 m. Each half has legs 3 m and 4 m, so the equal triangle legs are 5 m and the perimeter is 16 m.
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Frequently asked questions
Which side is A?
A is the base, opposite the angle between the equal legs. Each equal leg is labelled B on this page.
Can height be longer than an equal leg?
No. The equal leg is the hypotenuse of a right half-triangle and must exceed the height.
Does height and area determine the whole triangle?
Yes for an isosceles triangle: they fix the base, and symmetry fixes the equal legs and all angles.