Answer
$12 \pi \ in.^2$
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: $A=\pi r^2 \times \dfrac{Measure \ of \ the \ arc}{360^{\circ}}...(1)$
We are given that radius $r=12\ in. $ and $Measure \ of \ the \ arc=30^{\circ}$
Plug the data in the equation (1) to obtain:
$A=\pi (12)^2 \times \dfrac{30^{\circ}}{360^{\circ}}$
Therefore, we get , $Area=12 \pi \ in.^2$
