[tex]\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}}[/tex]
