Answer:
[tex]s \approx 282.20ft^2[/tex]
Step-by-step explanation:
A circle is a curve made up of all the points that are the same distance from the center. In this problem, we are asked to find the area of the sector. A sector is a region of a circle between two radii. Suppose you have a central angle [tex]\theta[/tex] degrees, the sector can be found as:
[tex]s=\frac{\theta}{360}\times\pi r^{2}[/tex]
We know:
[tex]r=14ft \\ \\ \theta=165^{\circ}[/tex]
So:
[tex]s=\frac{165^{\circ}}{360^{\circ}}\times\pi (14^{2}) \\ \\ s=\frac{11}{24}\times (196\pi) \\ \\ s=\frac{539}{6}\pi \approx 282.20ft^2[/tex]
