#### Answer

$12 \pi \ ft^2$

#### Work Step by Step

Let $A$ be the area of a sector of a circle . The area $(A)$ of a sector of a circle whose radius is $r$ is given by: $A=\pi r^2 \times \dfrac{Measure \ of \ the \ arc}{360^{\circ}}...(1)$
We are given that radius $r=4 \ ft $ and $Measure \ of \ the \ arc=360^{\circ}-90^{\circ}=270^{\circ}$
Plug the data in the equation (1) to obtain:
$A=\pi (4)^2 \times \dfrac{270^{\circ}}{360^{\circ}}$
Therefore, we get , $Area=12 \pi \ ft^2$