Answer:
Area = 18π cm²
Step-by-step explanation:
The shaded region is a sector of a circle with radius 9 cm.
[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}[/tex]
From inspection of the give diagram:
Substitute the values into the formula for area of a sector:
[tex]\implies A=\left(\dfrac{80^{\circ}}{360^{\circ}}\right) \pi \cdot 9^2[/tex]
[tex]\implies A=\dfrac{2}{9} \pi \cdot 81[/tex]
[tex]\implies A=\dfrac{162}{9} \pi[/tex]
[tex]\implies A=18 \pi\;\; \f cm^2[/tex]
Therefore, the area of the shaded region is 18π cm².
