Micah is going to paint his woodworking shop. The shop is a rectangular prism. The dimensions of the shop are shown in the diagram.
15.8ft 7.9ft 9ft
Including the doors, what is the lateral surface area of the shop in square feet?
A 676.24 ft2
B 213.3 ft2
C 426.6 ft2
D 1,123.38 ft2
The lateral surface area of a rectangular prism can be found by adding up the areas of all four sides.
The dimensions of the shop are 15.8ft, 7.9ft, and 9ft.
The two shorter sides have heights of 7.9ft and 9ft, so their areas are 7.9ft * 9ft = 71.1ft² and 7.9ft * 9ft = 71.1ft² respectively.
The two longer sides have heights of 7.9ft and 9ft, so their areas are 7.9ft * 15.8ft = 124.82ft² and 9ft * 15.8ft = 142.2ft² respectively.
Adding up all four areas, 71.1ft² + 71.1ft² + 124.82ft² + 142.2ft² = 409.22ft².
Therefore, the lateral surface area of the shop is 409.22ft².
Including the doors, this value will increase, but the exact area of the doors is not given in the information provided.
which answer choice is the correct answer and please double check before answering
I apologize for the confusion in my previous response.
To calculate the lateral surface area of the shop, we need to find the area of all four sides, excluding the top and bottom faces.
The two shorter sides have dimensions of 7.9ft (height) and 9ft (length), so their combined area is 7.9ft * 9ft = 71.1ft².
The two longer sides have dimensions of 15.8ft (height) and 9ft (length), so their combined area is 15.8ft * 9ft = 142.2ft².
Adding up the areas of the four sides, we get 71.1ft² + 71.1ft² + 142.2ft² + 142.2ft² = 426.6ft².
Therefore, the correct answer is C) 426.6 ft², which represents the lateral surface area of the shop, including the doors.