Answer: Choice C) 2,384 square inches
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Step-by-step explanation:
The front face is a triangle with area 168 since
A = b*h/2
A = 14*24/2
A = 336/2
A = 168
The back face is also a triangle, congruent to the one up front. Therefore the two faces have the same area leading to a total area of 168*2 = 336. This is the total base area.
The lateral surface area (LSA) is found through the formula below
LSA = p*d
where p is the perimeter of the triangular base face and d is the depth of the prism. In this case, the perimeter is p = 14+25+25 = 64 and the depth is d = 32
So this means the LSA is...
LSA = p*d
LSA = 64*32
LSA = 2048
Which adds onto the total base area we got earlier to get
total surface area = (total base area) + (LSA)
total surface area = (336) + (2048)
total surface area = 2384
The units are in square inches because surface area is just area but the combined individual areas of each face. Think of it like determining how much wrapping paper you'll need or how much paint is needed to coat the surface (the paint has the same thickness everywhere; there are no gaps or overlaps)