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Tyler is preparing to paint the shed in his backyard. The shed is a rectangular prism. He plans to paint all sides EXCEPT the side that sits on the ground. The length of the shed is 16 feet. The width of the shed is 25.5 feet. The height of the shed it 8 feet. In order to know how much paint to buy, Tyler must find the surface area that needs to be painted.

Explain the steps to find the surface area that needs to be painted AND tell what the surface area is that needs to be painted.

(4 points) write it simply

1 answer

To find the surface area that needs to be painted for Tyler's shed, follow these steps:

  1. Identify the dimensions of the shed:

    • Length (L) = 16 feet
    • Width (W) = 25.5 feet
    • Height (H) = 8 feet

  2. Calculate the surface area of all sides of the rectangular prism:
    A rectangular prism has 6 sides. The formula for the surface area (SA) of a rectangular prism is: \[ SA = 2(LW + LH + WH) \]

  3. Calculate each area:

    • LW = Length × Width = 16 × 25.5 = 408 square feet (this is the bottom area and will not be painted).
    • LH = Length × Height = 16 × 8 = 128 square feet (this is one of the longer sides).
    • WH = Width × Height = 25.5 × 8 = 204 square feet (this is one of the shorter sides).

  4. Add the areas of the sides to be painted:

    • The shed has 2 sides of length and height (LH) and 2 sides of width and height (WH):
    • Total area to paint = 2(LH) + 2(WH)
    • Calculating: \[ 2(128) + 2(204) = 256 + 408 = 664 \text{ square feet} \]

  5. Final Result: The surface area that needs to be painted is 664 square feet.

So, Tyler will need to buy enough paint for 664 square feet.