Reckoning / Shape / Triangle from three sides
Plane figure · Triangles
Triangle from three sides
Any triangle. With only the three sides known, the area comes from Heron’s formula.
Dimensions
Results
area A
perimeter P
Formulas
Heron (about 60 AD) showed the area follows from the sides alone. The sides must satisfy the triangle inequality: each shorter than the other two together, or the square root has nothing to take.
Checked: the A formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.
Topology lens
Topologically a disc, like every figure here without a hole: Euler characteristic 1. Stretching turns it into a circle, a square or a star. More on the lens.