Heron's formula

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

Result unit: area units

What it describes

The area of a triangle from the lengths of its three sides (

s

is the semiperimeter).

P

area

a, b, c

sides

s

semiperimeter

Area from the side lengths alone — without heights or angles;

s

is the semiperimeter. Useful when you only know the three sides.

You know all three sides but have no angles or heights.

The sides of a triangle are 3, 4, 5. Find the area using Heron's formula.

Substitution

s=\dfrac{3+4+5}{2}=6

Result

P=\sqrt{6\cdot3\cdot2\cdot1}=\sqrt{36}=6

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