Answer:
[tex]\large\boxed{A=40\pi\ in^2}[/tex]
Step-by-step explanation:
[tex]\dfrac{72^o}{360^o}=\dfrac{1}{5}[/tex]
[tex]\text{The shaded region is}\ \dfrac{2}{5}\ \text{of the whole circle.}\\\text{Therefore the area of the shaded region is}\ \dfrac{2}{5}\ \text{of the area of a circle.}\\\\\text{The formula of an area of a circle:}\\\\A_O=\pi r^2\\\\r-radius\\\\\text{Therefore the area of a shaded region is}\ A=\dfrac{2}{5}\pi r^2.\\\\\text{We have}\ r=10\ in.\\\\\text{Substitute:}\\\\A=\dfrac{2}{5}\pi(10^2)=\dfrac{2}{5}\pi(100)=\dfrac{200}{5}\pi=40\pi\ in^2[/tex]
