Answer
$ A=\frac{C^2}{4\pi}$
Work Step by Step
Let $ r $ be the radius of a circle; the area $ A $ and circumference $ C $ are:
$ A=\pi r^2$ and $ C=2\pi r $.
Rewrite the second equation as $ r=\frac{C}{2\pi}$
Plug it into the first one: $ A=\pi\times(\frac{C}{2\pi})^2=\frac{C^2}{4\pi}$
