The area of a circle is given by:
[tex]A=\pi r^2[/tex]and the circunference is given by:
[tex]C=2\pi r[/tex]So we can solve the equation of the circunference for r so:
[tex]r=\frac{C}{2\pi}[/tex]Now we can replace this expression for r in the area equation so:
[tex]A=\pi(\frac{C}{2\pi})^2[/tex]and finally we simplify it so:
[tex]A=\frac{\pi C^2}{4\pi^2}=\frac{C^2}{4\pi}[/tex]