The area of a sector is given by the formula:
[tex]\text{Area = }\frac{\theta}{360}\text{ }\pi r^2[/tex]From the circle shown:
[tex]\begin{gathered} \text{The radius, r = 4 ft} \\ \text{Angle of the sector, }\theta\text{ = 360 - 90} \\ \theta=270^0 \end{gathered}[/tex]Substitute r = 4 and θ = 270 into the formula given above:
[tex]\begin{gathered} \text{Area = }\frac{270}{360}\times3.14159\times4^2 \\ \text{Area = }37.699ft^2 \end{gathered}[/tex]