96 ft²
Step-by-step explanation:
As the base of the prism (the triangle) is an equilateral triangle (the sides are the same length), the surface area of the prism comprises:
- 3 congruent rectangles
- 2 congruent triangles
Area of a rectangle = width × length
⇒ area of the rectangle = 3 ft × 10 ft = 30 ft²
Area of a triangle = 1/2 × base × height
⇒ area of the triangle = 1/2 × 3 ft × 2 ft = 3 ft²
Total surface area = 3 × area of the rectangle + 2 × area of the triangle
= 3 × 30 ft² + 2 × 3 ft²
= 90 ft² + 6 ft²
= 96 ft²