The area of Tomas' rug is 54 square feet, which is smaller than the 324 square feet area of the living room. The calculations involve unit conversion from yards to feet for accurate comparison.
The area of the rug Tomas bought is calculated by multiplying its length by its width. Since we are given the dimensions in yards and the area of the room in square feet, we first need to convert the measurements to the same units.
1 yard = 3 feet, therefore:
3 yards x 3 feet/yard = 9 feet,
2 yards x 3 feet/yard = 6 feet.
The area of the rug in square feet is therefore:
9 feet x 6 feet = 54 square feet.
Comparing the area of the rug to the area of the room, which is 324 square feet, we see that the area of the rug is smaller than the area of the room.
The area of the rug is 54 ft2, which is smaller than the area of the room.