Answer
$40.5 \pi \ yd^2$
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 $r=18 \ yd$ and $Measure \ of \ the \ arc=45^{\circ}$
Plug the data in the equation (1) to obtain:
$A=\pi (18)^2 \times \dfrac{45^{\circ}}{360^{\circ}}=40.5 \pi \ yd^2$
Therefore, we get , $Area=40.5 \pi \ yd^2$
