Question

Find the exact area of a circle having the given circumference. 4(√3 π) A =

Answer 1

$\bf \textit{circumference of a circle}\\\\ C=2\pi r\qquad \begin{cases} r=radius\\ ----------\\ C=4\sqrt{3}\ \pi \end{cases}\implies 4\sqrt{3}\ \pi=2\pi r \\\\\\ \cfrac{4\sqrt{3}\ \pi}{2\pi}= \boxed{r}\\\\ -----------------------------\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \boxed{r}=\cfrac{4\sqrt{3}\ \pi}{2\pi}\implies A=\pi \left( \cfrac{4\sqrt{3}\ \pi}{2\pi} \right)^2$