Trigonometry
Intermediate

Heron's Formula

Triangle area from the three side lengths, where s is the semi-perimeter.

Formula

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

Variables

a,b,cSides
s(a+b+c)/2

Example

a=3,b=4,c=5 ⇒ 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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