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Mathematics

1 answer:

Step2247 [10]3 years ago

5 0

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

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

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

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