A rectangular room measures 12 feet in length and 9 feet in width. The owner decides to install carpet within the entire area of the room. To calculate the area that needs to be carpeted, use the formula for the area of a rectangle:
$$ A = l imes w $$
Where:
$A$ = area, $l$ = length, and $w$ = width. What is the area of the carpet required in square feet?