Question
Question
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)
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)
Answers
GPT-4o mini
To find the surface area of the shed that needs to be painted, we will 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 shed**:
The shed is a rectangular prism and has six faces: top, bottom, and four side walls. However, since Tyler is not painting the bottom face (the one on the ground), we will only calculate the top and the four side walls.
- **Area of the top face**:
\[
\text{Area}_{\text{top}} = L \times W = 16 \times 25.5 = 408 \text{ square feet}
\]
- **Area of the front and back faces**: These are the two vertical walls on the shorter sides (length).
\[
\text{Area}_{\text{front/back}} = 2 \times (L \times H) = 2 \times (16 \times 8) = 2 \times 128 = 256 \text{ square feet}
\]
- **Area of the left and right faces**: These are the two vertical walls on the longer sides (width).
\[
\text{Area}_{\text{left/right}} = 2 \times (W \times H) = 2 \times (25.5 \times 8) = 2 \times 204 = 408 \text{ square feet}
\]
3. **Calculate the total area that needs to be painted**:
Now, we add up the areas of the top face and the four side walls to find the total surface area to be painted:
\[
\text{Total Surface Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{front/back}} + \text{Area}_{\text{left/right}} = 408 + 256 + 408
\]
\[
\text{Total Surface Area} = 408 + 256 + 408 = 1072 \text{ square feet}
\]
**Conclusion**:
The surface area of the shed that needs to be painted is **1072 square feet**.
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 shed**:
The shed is a rectangular prism and has six faces: top, bottom, and four side walls. However, since Tyler is not painting the bottom face (the one on the ground), we will only calculate the top and the four side walls.
- **Area of the top face**:
\[
\text{Area}_{\text{top}} = L \times W = 16 \times 25.5 = 408 \text{ square feet}
\]
- **Area of the front and back faces**: These are the two vertical walls on the shorter sides (length).
\[
\text{Area}_{\text{front/back}} = 2 \times (L \times H) = 2 \times (16 \times 8) = 2 \times 128 = 256 \text{ square feet}
\]
- **Area of the left and right faces**: These are the two vertical walls on the longer sides (width).
\[
\text{Area}_{\text{left/right}} = 2 \times (W \times H) = 2 \times (25.5 \times 8) = 2 \times 204 = 408 \text{ square feet}
\]
3. **Calculate the total area that needs to be painted**:
Now, we add up the areas of the top face and the four side walls to find the total surface area to be painted:
\[
\text{Total Surface Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{front/back}} + \text{Area}_{\text{left/right}} = 408 + 256 + 408
\]
\[
\text{Total Surface Area} = 408 + 256 + 408 = 1072 \text{ square feet}
\]
**Conclusion**:
The surface area of the shed that needs to be painted is **1072 square feet**.