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 length 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)

Question

Responses

228 ft2
228 ft squared

48 ft2
48 ft squared

180 ft2
180 ft squared

132 ft2

Answer 1

To determine the amount of wallpaper Katerina needs to purchase, we first need to calculate the total area of the wall and then subtract the area of the windows.

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 one window: $$\text{Area of one window}=\text{height}\times \text{length}=6,\text{ft}\times 4,\text{ft}=24,{\text{ft}}^2$$

3. Calculate the area of both windows: $$\text{Area of both windows}=2\times 24,{\text{ft}}^2=48,{\text{ft}}^2$$

4. Subtract the area of the windows from the area of the wall to find the area that needs to be covered with wallpaper: $$\text{Area to be covered}=\text{Area of the wall}-\text{Area of both windows}=180,{\text{ft}}^2-48,{\text{ft}}^2=132,{\text{ft}}^2$$

Thus, Katerina should purchase 132 ft² of wallpaper.

The correct response is 132 ft².