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
