Micah is going to paint his woodworking shop. The shop is a rectangular prism. The dimensions of the shop are shown in the diagram.
15.8 ft, 9 ft., 7.9 ft
including the doors, what is the lateral surface area of the shop in square feet?
a 676.24 ft^2
b 213.3 ft^2
c 426.6 ft^2
d 1,123.38 ft^2
The lateral surface area of a rectangular prism can be found by finding the sum of the areas of the four sides (excluding the top and bottom). The dimensions of the shop are given as 15.8 ft, 9 ft, and 7.9 ft.
The sum of the areas of the four sides can be calculated as follows:
2(15.8 ft * 9 ft) + 2(15.8 ft * 7.9 ft) + 2(9 ft * 7.9 ft)
Evaluating the above expression, we get:
2(142.2 ft²) + 2(124.82 ft²) + 2(71.1 ft²)
284.4 ft² + 249.64 ft² + 142.2 ft²
676.24 ft²
Therefore, the lateral surface area of the shop, including the doors, is 676.24 ft².
The correct answer is a) 676.24 ft².