Answer: area ≈ 59.441 in²lateral area ≈ 352.671 in²surface area ≈ 471.553 in²Step-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 sidesFilling 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 . . . inchesThen 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