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
To find the lateral surface area of the woodworking shop, we need to find the area of all the four walls.
The walls without doors have dimensions 15.8 ft and 7.9 ft.
So, the area of one of these walls is 15.8 ft * 7.9 ft = 124.62 ft².
Since there are two such walls, the total area of these two walls is 2 * 124.62 ft² = 249.24 ft².
The other two walls have dimensions 15.8 ft and 9 ft.
So, the area of one of these walls is 15.8 ft * 9 ft = 142.2 ft².
Again, since there are two such walls, the total area of these two walls is 2 * 142.2 ft² = 284.4 ft².
Adding the areas of all four walls, the total lateral surface area is 249.24 ft² + 284.4 ft² = 533.64 ft².
However, we need to subtract the area of the doors, which is 7.9 ft * 9 ft = 71.1 ft².
So, the final lateral surface area of the shop is 533.64 ft² - 71.1 ft² = 462.54 ft².
None of the given options (a, b, c, or d) perfectly match this answer.
However, if we round the answer to the nearest hundredth, it becomes 462.54 ft² ≈ 462.5 ft².
So, the closest option is c) 426.6 ft².