Answer:
1032 square inches
Explanation:
You want the surface area of a triangular prism with a length of 17 inches and a triangular base that has a base of 18 inches and height of 12 inches. The other two sides of the triangle are 15 inches.
Area
The surface area of the prism is the sum of the two triangular base areas and the areas of the rectangular faces. In a formula, that is ...
SA = 2B +Ph
where B is the area of one triangular base, P is the perimeter of the base, and h is the length of the prism.
Base area
The triangular base area is ...
B = 1/2bh = 1/2(18 in)(12 in) = 108 in²
Lateral area
The perimeter of the triangular base is ...
P = 18 + 15 + 15 = 48 . . . . inches
Then the area of the rectangular faces is ...
Ph = (48 in)(17 in) = 816 in²
Total surface area
Now, we have the numbers to use in our area formula:
SA = 2B +Ph
SA = 2(108 in²) +816 in² = 1032 in²
The surface area of the triangular prism is 1032 square inches.
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