Answer:
- 6 ft² — each base
- 12 ft² — total base area
- 144 ft² — lateral area
- 156 ft² — total surface area
Step-by-step explanation:
You are given the formulas for computing the area of a triangular prism, along with dimension values filled in. You need only to perform the arithmetic.
Base area
Thea area of each base is ...
A = 1/2(b)(h) = 1/2(3)(4) = 6 . . . . ft²
There are 2 bases, so the total base area is ...
A = 2(6 ft²) = 12 ft²
Lateral area
The lateral area is the sum of the areas of each of the rectangular faces. For triangle sides of a, b, c, and prism height h, the lateral area is ...
A = (h)(a) +(h)(b) +(h)(c) = (12)(3) +(12)(5) +(12)(4) = 144 . . . ft²
Total area
The total area is the sum of the base area and the lateral area:
total area = (12 ft²) +(144 ft²) = 156 ft²
