Geometry & Trigonometry
Intermediate

Heron's Formula

Area of a triangle from its three sides, s = (a+b+c)/2.

Formula

A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}

Variables

a, b, cSides
sSemi-perimeter

Example

Triangle 3, 4, 5: s = 6, A = √(6·3·2·1) = √36 = 6.

Did You Know?

Heron's formula finds a triangle's area from its three sides alone — no height or angle needed.

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