Question
Katerina is purchasing wallpaper to cover one wall in her bedroom. The wall is rectangular in shape, with a height of 10 ft. and a lenght of 18 ft. The wall contains two rectangular windows that are 6 ft. by 4 ft each. Determine the amount of wallpaper that Katerina should purchase to cover the wall. (1 point)
Responses
122 ft2
2
122 ft2
22 ft2
2
22 ft2
132 ft2
2
132 ft2
32 ft2
Responses
122 ft2
2
122 ft2
22 ft2
2
22 ft2
132 ft2
2
132 ft2
32 ft2
Answers
GPT-4o mini
To calculate the amount of wallpaper Katerina needs to cover the wall, we can follow these steps:
1. **Calculate the area of the wall**:
\[
\text{Area of the wall} = \text{height} \times \text{length} = 10 \text{ ft} \times 18 \text{ ft} = 180 \text{ ft}^2
\]
2. **Calculate the area of the windows**:
Each window has dimensions of 6 ft by 4 ft:
\[
\text{Area of one window} = 6 \text{ ft} \times 4 \text{ ft} = 24 \text{ ft}^2
\]
Since there are two windows:
\[
\text{Total area of windows} = 2 \times 24 \text{ ft}^2 = 48 \text{ ft}^2
\]
3. **Calculate the area to be covered by wallpaper**:
\[
\text{Area to be covered} = \text{Area of the wall} - \text{Total area of windows}
\]
\[
\text{Area to be covered} = 180 \text{ ft}^2 - 48 \text{ ft}^2 = 132 \text{ ft}^2
\]
Therefore, Katerina should purchase **132 ft²** of wallpaper to cover the wall. The correct response is:
**132 ft²**
1. **Calculate the area of the wall**:
\[
\text{Area of the wall} = \text{height} \times \text{length} = 10 \text{ ft} \times 18 \text{ ft} = 180 \text{ ft}^2
\]
2. **Calculate the area of the windows**:
Each window has dimensions of 6 ft by 4 ft:
\[
\text{Area of one window} = 6 \text{ ft} \times 4 \text{ ft} = 24 \text{ ft}^2
\]
Since there are two windows:
\[
\text{Total area of windows} = 2 \times 24 \text{ ft}^2 = 48 \text{ ft}^2
\]
3. **Calculate the area to be covered by wallpaper**:
\[
\text{Area to be covered} = \text{Area of the wall} - \text{Total area of windows}
\]
\[
\text{Area to be covered} = 180 \text{ ft}^2 - 48 \text{ ft}^2 = 132 \text{ ft}^2
\]
Therefore, Katerina should purchase **132 ft²** of wallpaper to cover the wall. The correct response is:
**132 ft²**
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