Question

Please help! And explain.

Answer 1

$\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}\qquad \begin{cases} \theta=\textit{angle in radians}\\ r=radius\\ ----------\\ r=5\\ \theta=\frac{\pi }{4} \end{cases}\implies A=\cfrac{\frac{\pi }{4}\cdot 5^2}{2}\\\\ -----------------------------\\\\ A=\cfrac{\frac{\pi }{4}\cdot 25}{2}\implies A=\cfrac{\frac{25\pi }{4}}{2}\implies A=\cfrac{\frac{25\pi }{4}}{\frac{2}{1}}\implies A=\cfrac{25\pi }{4}\cdot \cfrac{1}{2} \\\\\\ \boxed{A=\cfrac{25\pi }{8}}$