Find the area of the shaded regions. Give your answer as a completly simplified exact value in terms of pi

[tex]\boxed{\begin{array}{l}\underline{\textsf{Area of a sector}}\\\\A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the radius.}\\\phantom{ww}\bullet\;\;\textsf{$\theta$ is the angle measured in degrees.}\end{array}}[/tex]

Question 1

The shaded region of the given circle with a radius of 10 inches is made up of two congruent sectors, each with a central angle of 72°. Therefore, to find the area of the shaded region, substitute r = 10 and θ = 72° into the formula, and multiply it by 2:

[tex]\begin{aligned}A&=2 \cdot \left(\dfrac{72^{\circ}}{360^{\circ}}\right) \pi \cdot 10^2\\\\A&=2 \cdot \left(\dfrac{1}{5}\right) \pi \cdot 100\\\\A&=200 \cdot \left(\dfrac{1}{5}\right) \pi\\\\A&=\dfrac{200}{5} \pi\\\\A&=40\pi\; \sf in^2\end{aligned}[/tex]

Therefore, the exact area of the shaded region in terms of π is:

[tex]\Large\boxed{\boxed{40\pi \sf \; in^2}}[/tex]

Question 2

To find the area of the shaded region of a circle with a radius of 9 cm and a central angle of 80°, substitute r = 9 and θ = 80° into the formula:

[tex]\begin{aligned}A&= \left(\dfrac{80^{\circ}}{360^{\circ}}\right) \pi \cdot 9^2\\\\A&= \left(\dfrac{2}{9}\right) \pi \cdot 81\\\\A&= \dfrac{162}{9} \pi\\\\A&=18 \pi\; \sf cm^2\end{aligned}[/tex]

Therefore, the exact area of the shaded region in terms of π is:

[tex]\Large\boxed{\boxed{18\pi \sf \; cm^2}}[/tex]