Answer:
The total surface area is: 468 in^2 which agrees with answer a)
Explanation:
The three lateral faces of the prism are rectangles, and the sums of their areas give:
12 * 10 + 9 * 10 + 15 * 10 = 360 in^2
The area of each triangular base (notice it is a right triangle) is given by:
9 * 12 / 2 = 54 in^2, so we add TWO of these to the three rectangular faces:
Total surface = 360 in^2 + 2 * 54 in^2 = 468 in^2