Isoperimetric inequality

Statement

Let $\gamma$ be a simple closed curve in the Euclidean plane $\mathbb {R} ^{2}$. Let $Int(\gamma )$ denote the interior of $\gamma$. Let $l(\gamma )$ denote the length of $\gamma$. Then:

$4\pi Ar(Int(\gamma ))\leq l(\gamma )^{2}$

where $Ar$ is the area.

Equality holds if and only if $\gamma$ is a circle.