Question

what is the surface area of the prism in square inches?

Answer 1

Given:

Given that the triangular prism with height 10 inches.

The side lengths of the base of the triangle are 12 inches, 13 inches and 5 inches.

We need to determine the surface area of the prism.

Surface area of the prism:

The surface area of the prism can be determined using the formula,

$SA=bh+(s_1+s_2+s_3)H$

where b is the base and h is the height of the triangle.

s₁, s₂, s₃ are the side lengths of the triangle and

H is the height of the prism.

Substituting b = 12, h = 5, s₁ = 12, s₂ = 5, s₃ = 13 and H = 10 in the above formula, we get;

$SA=(12)(5)+(12+5+13)(10)$

$SA=60+(30)(10)$

$SA=60+300$

$SA=360 \ in^2$

Thus, the surface area of the triangular prism is 360 square inches.

Hence, Option b is the correct answer.