Heron's formula

In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths ${\displaystyle a,}$ ${\displaystyle b,}$ ${\displaystyle c.}$ Letting ${\displaystyle s}$ be the semiperimeter of the triangle, ${\displaystyle s={\tfrac {1}{2}}(a+b+c),}$ the area ${\displaystyle A}$ is

${\displaystyle A={\sqrt {s(s-a)(s-b)(s-c)}}.}$

It is named after first-century engineer Heron of Alexandria (or Hero) who proved it in his work Metrica, though it was probably known centuries earlier.