Answer:
Surface Area = 267 in²
V = 162 in³
Step-by-step explanation:
The surface area consists of 3 rectangles of the sides, and the two base triangles.
The front rectangle has dimensions of 12x9, so it's area is 108 in²
The back rectangle has dimensions of 7x12, so it's are is 84 in²
The side rectangle has dimensions of 4x12, so it's area is 48 in²
The top and bottom triangles have a base of 9 and a height of 3, so their area is
A = (1/2)(9)(3) = 27/2, but there are 2 of them, so their combined area is (27/2)(2) = 27 in²
The total surface area is 108 + 84 + 48 + 27 = 267 in²
The formula for volume of a triangular prism is
V = (1/2)bhd where b is the base of the base triangle, h is the height of the base triangle, and d is the depth of prism.
We have b = 9, h = 3, and d = 12, so the volume is
V = (1/2)(9)(3)(12)
V = (1/2)(27)(12)
V = (1/2)(324)
V = 162 in³
