Constantinos is painting a rectangular outline of a frame on the wall, leaving the area inside unpainted. He wants the outside of the frame to be 9 ft. wide by 12 ft. tall. The inside of the frame will be 6 ft. wide by 10 ft. tall. Calculate the area of the frame.(1 point)

Question

Responses

168 ft.2
168 ft. squared

48 ft.2
48 ft. squared

60 ft.2
60 ft. squared

108 ft.2

Answer 1

To calculate the area of the frame, we need to find the area of the outer rectangle (the entire frame including the painted area) and subtract the area of the inner rectangle (the unpainted area).

1. Calculate the area of the outer rectangle:

   • Width: 9 ft
   • Height: 12 ft \[ \text{Area}_{\text{outer}} = \text{width} \times \text{height} = 9 \text{ ft} \times 12 \text{ ft} = 108 \text{ ft}^2 \]

2. Calculate the area of the inner rectangle:

   • Width: 6 ft
   • Height: 10 ft \[ \text{Area}_{\text{inner}} = \text{width} \times \text{height} = 6 \text{ ft} \times 10 \text{ ft} = 60 \text{ ft}^2 \]

3. Calculate the area of the frame: \[ \text{Area}{\text{frame}} = \text{Area}{\text{outer}} - \text{Area}_{\text{inner}} = 108 \text{ ft}^2 - 60 \text{ ft}^2 = 48 \text{ ft}^2 \]

Therefore, the area of the frame is 48 ft.².