ANSWER
[tex]264in^2[/tex]
EXPLANATION
We have that the shaded sector is subtended at 210 degrees at the center of the circle that has a radius of 12 inches.
The area of a sector is given as:
[tex]\frac{A}{360}\cdot\text{ }\pi r^2[/tex]
where A = angle the sector subtends at the circle's center
So, we have that:
[tex]\begin{gathered} \frac{210}{360}\cdot\text{ }\pi\cdot12^2 \\ =263.89in^2 \\ \approx264in^2 \end{gathered}[/tex]
That is the answer.
