To find the area that the carpet needs to cover, we need to calculate the area of the living room that is not covered by the tiled floor.
The tiled floor measures 5 3/4 ft by 3 1/2 ft, so to find the area we can use the formula for area of a rectangle:
Area = Length x Width
Area of the tiled floor = 5 3/4 ft x 3 1/2 ft = 20.25 ft^2
So the area that the carpet needs to cover is 20.25 ft^2.