Question

A triangular prism has an equilateral triangle base whose side length is 6 in. The height of the prism is 10 in. Which of the following correctly calculates the surface area of this triangular prism?(1 point)
Responses

182.60 in.2

182.60 in. squared

211.18 in.2

211.18 in. squared

271.14 in.2

271.14 in. squared

304.56 in.2

Answer 1

Surface area = 2·(area of equilateral triangle) + (perimeter of triangle)·(prism height).
Area triangle = (√3/4)·6^2 = 9√3 ≈ 15.5885, so 2·area = 18√3 ≈ 31.177.
Perimeter = 3·6 = 18, lateral area = 18·10 = 180.
Total SA = 180 + 18√3 ≈ 211.18 in^2.

Answer: 211.18 in.²