Question

The perimeter of a semicircle is 5.14 feet. What is the semicircle’s area?

Answer 1

$\bf \textit{circumference of a semi-circle}\\\\ C=\pi r\qquad \begin{cases} r=radius\\ -----\\ C=5.14 \end{cases}\implies 5.14=\pi r\implies \boxed{\cfrac{5.14}{\pi }=r}\\\\ -------------------------------\\\\ \textit{area of a semi-circle}\\\\ A=\cfrac{\pi r^2}{2} \implies A=\cfrac{\pi }{2}r^2\implies A=\cfrac{\pi }{2}\left( \boxed{\cfrac{5.14}{\pi }} \right)^2 \\\\\\ A=\cfrac{\pi }{2}\implies \cfrac{5.14^2}{\pi ^2}\implies A=\cfrac{26.4196}{2\pi }\implies A=\cfrac{13.2098}{\pi }$