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:The surface area = 211.2 inches²Step-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