Answer: The required area of the room that is NOT covered by the carpet is 192 ft².
Step-by-step explanation: Given that the Smith wants to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.
We are to find the area of the room that is NOT covered by the carpet.
We know that the area of a rectangle is given by the product of its length and breadth.
So, the area of the carpet bought by Smith is
[tex]A_c=9\times12=108~\textup{ft}^2,[/tex]
and the are of the room is
[tex]A_r=15\times 20=300~\textup{ft}^2.[/tex]
Therefore, area of the room that is NOT covered by the carpet will be
[tex]A=A_r-A_c=300-108=192~\textup{ft}^2.[/tex]
Thus, the required area of the room that is NOT covered by the carpet is 192 ft².
