Question

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

Answer 1

Answer:

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