<u>Given</u>:
Given that the radius of the circle is 16 ft.
We need to determine the area of the shaded sector of the circle.
<u>Angle of the shaded region:</u>
The angle of the shaded region is given by
![\theta=360-90=270](https://tex.z-dn.net/?f=%5Ctheta%3D360-90%3D270)
Thus, the angle of the shaded region of the circle is 270°
<u>Area of the shaded sector of the circle:</u>
The area of the shaded sector of the circle can be determined using the formula,
![A=(\frac{\theta}{360}) \pi r^2](https://tex.z-dn.net/?f=A%3D%28%5Cfrac%7B%5Ctheta%7D%7B360%7D%29%20%5Cpi%20r%5E2)
Substituting r = 16 and
, we have;
![A=(\frac{270}{360})(3.14)(16)^2](https://tex.z-dn.net/?f=A%3D%28%5Cfrac%7B270%7D%7B360%7D%29%283.14%29%2816%29%5E2)
![A=(\frac{270}{360})(3.14)(256)](https://tex.z-dn.net/?f=A%3D%28%5Cfrac%7B270%7D%7B360%7D%29%283.14%29%28256%29)
![A=602.88 \ ft^2](https://tex.z-dn.net/?f=A%3D602.88%20%5C%20ft%5E2)
Thus, the area of the shaded sector of the circle is 602.88 square feet.