Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6 in. The height of the prism is 10 in

The surface area = 211.2 inches²

Step-by-step explanation:

* Lets explain how to solve the problem

- The prism has triangular base

- The base is equilateral triangle

- The surface area of any prism = lateral area + 2 base area

- The lateral area = perimeter of base * its height

- The perimeter of the equilateral triangle = 3L, where L is the length

of its side

∴ The lateral area = 3L * h = 3Lh

- Area of the equilateral triangle = 1/2 * L * L * sin (60)

Area of the equilateral triangle = 1/2 * L * L * √3/2

Area of the equilateral triangle = √3/4 L²

∴ The surface area = 3Lh + 2 (√3/4 L²) = 3Lh + √3/2 L²

∵ The side length (L) of the equilateral Δ = 6 inches

∵ The height (h) of the prism = 10 inches

∴ The surface area = 3 (6) (10) + √3/2 (6²)

∴ The surface area = 180 + 18√3 = 211.18

* The surface area = 211.2 inches²