Answer:
1200 in²
Step-by-step explanation:
The surface area of the prism is the sum of the lateral area and the areas of the bases.
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<h3>lateral area</h3>
The lateral area is the total area of the three rectangular faces. It can be computed from ...
LA = Ph
where P is the perimeter of the triangular base, and h is the height of the prism (the distance between triangular bases).
The perimeter is the sum of the edge lengths of the base:
P = 30 in + 17 in + 17 in = 64 in
Then the lateral area is ...
LA = (64 in)(15 in) = 960 in²
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<h3>base area</h3>
The two bases are congruent triangles, so have a total area of ...
A = 2(1/2bh) = bh
where b is the base of the triangle, and h is its height.
A = (30 in)(8 in) = 240 in²
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<h3>total surface area</h3>
The sum of lateral area and base area is ...
total area = (960 in²) +(240 in²) = 1200 in²
The surface area of the triangular prism is 1200 square inches.
