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=(\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=(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