Micah is going to paint his woodworking shop. The shop is a rectangular prism. The dimensions of the shop are shown in the diagram.
height is 9ft
length is 15.8ft
witth is 7.9 fr
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 multiplying the perimeter of the base by the height.
The perimeter of the base can be found by adding together all the sides of the rectangle.
Perimeter of the base = 2 * (length + width)
Perimeter of the base = 2 * (15.8ft + 7.9ft)
Perimeter of the base = 2 * 23.7ft
Perimeter of the base = 47.4ft
Lateral surface area = Perimeter of the base * height
Lateral surface area = 47.4ft * 9ft
Lateral surface area = 426.6 ft^2
Therefore, the lateral surface area of the shop is 426.6 ft^2, which corresponds to option C.