Question

A student is painting a doghouse like the rectangular prism shown.

A rectangular prism with base dimensions of 7 feet by 5 feet. It has a height of 4 feet.

Part A: Find the total surface area of the doghouse. Show your work. (3 points)

Part B: If one can of paint will cover 50 square feet, how many cans of paint are needed to paint the doghouse? Explain. (Hint: The bottom will not be painted since it will be on the ground.) (1 point)

Answer 1

Part A

Surface area of a rectangular prism = 2(lw + lh + wh).

Here l = 7 ft, w = 5 ft, h = 4 ft:
lw = 7·5 = 35
lh = 7·4 = 28
wh = 5·4 = 20

Surface area = 2(35 + 28 + 20) = 2(83) = 166 ft².

Total surface area = 166 ft².

Part B

Do not paint the bottom (area = lw = 35 ft²), so area to be painted = 166 − 35 = 131 ft².

Each can covers 50 ft², so number of cans = ceil(131/50) = ceil(2.62) = 3 cans.

So 3 cans of paint are needed.