Begin by finding the area of the octagon. We can do this by finding the area of the square that would encompass the octagon which has side lengths of 7 inches. 7x7=49 square inches, and then we can subtract the area of the 4 triangular corners. The 4 corners are right triangles with side lengths b=2 in and h=2 in. Using A=1/2bh, the corners' area are each 1/2x2x2 = 2 square inches. Now subtract:
49 in^2 - (4 x 2 in^2) = 41 in^2
To answer Question A, all we have to do is multiply the area of the octagon by the prism's height.
41 in^2 x 7 in = 287 in^3
For Question B, we have to solve for the height in the equation we used in Question A, Volume = Area x Height. Using 123 in^3 as our volume, our equation looks as follows:
123 in^3 = 41 in^2 x Height
We can then divide 123 in^3 by 41 in^2 to get the answer of 3 in.