According to the problem, and using the central angle theorem, we know that the central angle is 135°.
Then, we use the following formula
[tex]\begin{gathered} A=\pi(r)^2\cdot\frac{\theta}{360} \\ A=\pi(4)^2\cdot\frac{135}{360} \\ A=\pi\cdot16\cdot\frac{135}{360} \\ A=6\pi(ft)^2 \end{gathered}[/tex]
Hence, the area of the shaded sector is 6pi square feet.
