Question

Formula for the area of a circle in terms of its circumference

Answer 1

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