[tex]\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=77.62 \end{cases}\implies 77.62=2\pi r\implies \cfrac{77.62}{2\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi \left( \cfrac{77.62}{2\pi } \right)^2\implies A=\cfrac{77.62^2}{4\pi }\implies A\approx 479.69[/tex]
