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<u>Given</u>:
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.
<u>Surface area of the prism:</u>
The surface area of the prism can be determined using the formula,
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;
Thus, the surface area of the triangular prism is 360 square inches.
Hence, Option b is the correct answer.