Answer:
5,864.31 ft²
Step-by-step explanation:
The area of a full circle is given by:
[tex]A_C=\pi r^2[/tex]
Since the room is a circular sector with a central angle of 105 degrees and knowing that a circle has a central angle of 360 degrees, the area of the room is:
[tex]A_R=\frac{105}{360} \pi r^2=\frac{105}{360} \pi 80^2\\A_R = 5,864.31\ ft^2[/tex]
The area of the carpet to be laid is 5,864.31 ft².
