Answer
$24 \pi \ in.^2$
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: $A=\pi r^2 \times \dfrac{Measure \ of \ the \ arc}{360^{\circ}}$ or, $A_{Top}=\pi r^2 \times \dfrac{m \widehat{PT}}{360^{\circ}}..(1)$
Radius, $r=8 \ in.$ and $m \widehat{PT}=135^{\circ}$
Plug the data in the equation (1) to obtain:
$A_{TOP}=\pi (8)^2 \times \dfrac{135^{\circ}}{360^{\circ}}$
Therefore, we get , $Area=24 \pi \ in.^2$
