Question

Represent the area of the Circle as a function of its circumference

Answer 1

$\bf \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \boxed{\cfrac{C}{2\pi }=r} \\\\\\ \textit{area of a circle}\\\\ A=\pi r^2\implies A=\pi \left( \boxed{\cfrac{C}{2\pi} } \right)^2\implies A=\pi \cdot \cfrac{C^2}{2^2\pi^2}\implies A=\cfrac{C^2}{4\pi }$