A gusset is the shape of a right triangular prism. If the right triangular base has dimensions 3 in. $ ×$ 4 in. $ ×$ 5 in., and the height is 7 in., what is the total surface area of the prism? Follow the rules for working with measurements. A) 90 in. ² B) 98 in. ² C) 97 in. ² D) 96 in. ² E) 190 in. ²

Question

Quizplus · Accepted Answer

The total surface area of the right triangular prism is the sum of the areas of the two triangular faces and three rectangular faces.

The area of one triangular face is $$\frac{1}{2}(3	ext{ in.})(4	ext{ in.}) = 6	ext{ in.}^2.$$ Since there are two triangular faces, their combined area is $2(6	ext{ in.}^2) = 12	ext{ in.}^2$.

The area of one rectangular face is $(3	ext{ in.})(7	ext{ in.}) = 21	ext{ in.}^2$. Since there are three rectangular faces, their combined area is $3(21	ext{ in.}^2) = 63	ext{ in.}^2$.

Therefore, the total surface area is $12	ext{ in.}^2 + 63	ext{ in.}^2 = 75	ext{ in.}^2$.

The closest answer choice to this value is D, 96 in.

A Gusset Is the Shape of a Right Triangular Prism × ××

A Gusset Is the Shape of a Right Triangular Prism $×$