Heron's formula

In geometry, Heron's formula states that the area of a triangle whose sides have lengths a, b, c is

${\sqrt {s\left(s-a\right)\left(s-b\right)\left(s-c\right)}}$

where

$s={\frac {a+b+c}{2}}$

This formula is credited to Heron of Alexandria, although it is possible that it may have been known long before Heron's time.

The formula is in fact a special case of Brahmagupta's formula for the area of a cyclic quadrilateral; both of which are special cases of Bretschneider's formula for the area of a quadrilateral.