<u>Given</u>:
Given that the radius of the circle is 12 inches.
The angle of the shaded sector is 210°
We need to determine the area of the shaded sector.
<u>Area of the shaded sector:</u>
The area of the shaded sector can be determined using the formula,
Substituting and r = 12, we get;
Simplifying, we get;
Thus, the area of the shaded sector is 263.9 square inches.
Hence, Option c is the correct answer.