Micah is going to paint his woodworking shop. The shop is a rectangular prism. The dimensions of the shop are shown in the diagram.
Including the doors, what is the lateral surface area of the shop in square feet?
In order to find the lateral surface area of the rectangular prism, we need to find the area of all four sides.
The dimensions of the shop are 10 feet wide, 7 feet high, and 20 feet long.
The front and back sides have dimensions 10 ft x 7 ft, so their combined area is 10 ft x 7 ft x 2 = 140 square feet.
The left and right sides have dimensions 20 ft x 7 ft, so their combined area is 20 ft x 7 ft x 2 = 280 square feet.
Adding the areas of all four sides, we get a lateral surface area of 140 square feet + 280 square feet = <<140+280=420>>420 square feet.
Therefore, the lateral surface area of the shop, including the doors, is 420 square feet.