Answer:
- area ≈ 59.441 in²
- lateral area ≈ 352.671 in²
- surface area ≈ 471.553 in²
Step-by-step explanation:
1. The area of the regular polygon base of the prism can be found from the formula ...
A = (nr²/2)sin(360°/n) . . . . where r is the radius and n is the number of sides
Filling in the numbers and doing the arithmetic gives ...
A = (5·5²/2)sin(72°) ≈ 59.441 . . . square inches
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2. The lateral area is the product of the height and the perimeter. The perimeter of the regular polygon can be found from ...
P = 2nr·sin(180°/n) = 50sin(36°) ≈ 29.389 . . . inches
Then the lateral area is ...
LA = Ph = (29.389 in)(12 in) = 352.671 in²
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3. The total area is the area of the two bases together with the lateral area:
S = 2·(base area) + (lateral area) = 2(59.441 in²) + 352.671 in²
S = 471.553 in²
