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

180 ft.2
180 ft. squared

132 ft.2
132 ft. squared

48 ft.2
48 ft. squared

228 ft.2

Answer 1

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

1. Calculate the area of the wall:

   • The wall is rectangular, so the area can be calculated using the formula: \[ \text{Area of wall} = \text{height} \times \text{length} = 10 , \text{ft} \times 18 , \text{ft} = 180 , \text{ft}^2 \]

2. Calculate the area of the windows:

   • Each window has an area of: \[ \text{Area of one window} = \text{height} \times \text{width} = 6 , \text{ft} \times 4 , \text{ft} = 24 , \text{ft}^2 \]
   • Since there are two windows: \[ \text{Total area of windows} = 2 \times 24 , \text{ft}^2 = 48 , \text{ft}^2 \]

3. Calculate the area that needs to be covered with wallpaper:

   • Subtract the area of the windows from the area of the wall: \[ \text{Area to cover} = \text{Area of wall} - \text{Total area of windows} = 180 , \text{ft}^2 - 48 , \text{ft}^2 = 132 , \text{ft}^2 \]

Thus, Katerina should purchase 132 ft² of wallpaper.

The correct response is: 132 ft.²