Question

Reference attached image for the problem.Please show your work for finding the partial area.

Answer 1

To find the area of a sector of a circle use the next formula:

$A=\frac{\theta}{360º}*\pi *r^2$

As the given circle has a outside angle 90º (it is not part of the sector of the circle) subtract the 90º from 360º (total angle of a circle) to find the angle of the sector:

$\theta=360º-90º=270º$

Find the area of the sector with angle 270º:

$\begin{gathered} A=\frac{270º}{360º}*3.14*(11in)\placeholder{⬚}^2 \\ \\ A=0.75*3.14*121in^2 \\ \\ A=284.955in^2 \end{gathered}$Then, the approximate area of the given sector of a circle is 284.955 square inches