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

60 ft.2
60 ft. squared

108 ft.2
108 ft. squared

48 ft.2
48 ft. squared

168 ft.2

Answer 1

To calculate the area of the frame, we need to find the area of the outer rectangle and subtract the area of the inner rectangle.

1. Calculate the area of the outer rectangle (which is 9 ft wide and 12 ft tall):

   \[ \text{Area}_{\text{outer}} = \text{width} \times \text{height} = 9 , \text{ft} \times 12 , \text{ft} = 108 , \text{ft}^2 \]

2. Calculate the area of the inner rectangle (which is 6 ft wide and 10 ft tall):

   \[ \text{Area}_{\text{inner}} = \text{width} \times \text{height} = 6 , \text{ft} \times 10 , \text{ft} = 60 , \text{ft}^2 \]

3. Calculate the area of the frame by subtracting the area of the inner rectangle from the area of the outer rectangle:

   \[ \text{Area}{\text{frame}} = \text{Area}{\text{outer}} - \text{Area}_{\text{inner}} = 108 , \text{ft}^2 - 60 , \text{ft}^2 = 48 , \text{ft}^2 \]

Thus, the area of the frame is 48 ft. squared.