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, 7.9, 9 ft
Including the doors, what is the lateral surface area of the shop in square feet?
Responses
A 676.24 ft2676.24 ft 2
B 213.3 ft2213.3 ft 2
C 426.6 ft2426.6 ft 2
D 1,123.38 ft2
The lateral surface area of a rectangular prism can be found by adding up the areas of all the side faces.
In this case, the side faces are the four walls of the shop (excluding the top and bottom faces) and the two doors.
The dimensions of the shop are given as 15.8 ft, 7.9 ft, and 9 ft.
The area of each wall face is found by multiplying the length by the width. The area of each door face is found by multiplying the height by the width.
The area of the four walls is (15.8 ft * 9 ft) + (7.9 ft * 9 ft) + (15.8 ft * 9 ft) + (7.9 ft * 9 ft) = 142.2 ft^2.
The area of the two doors is (15.8 ft * 7.9 ft) + (15.8 ft * 7.9 ft) = 249.32 ft^2.
Adding the areas of the walls and doors, the lateral surface area of the shop is 142.2 ft^2 + 249.32 ft^2 = 391.52 ft^2.
Therefore, the correct answer is C) 426.6 ft^2.