If your sketch is 25 times smaller than your room, then your room is 25 times larger than your sketch. That means your room is 3.84 x 25 or 96 inches in one direction and 3.6 x 25 or 90 inches in the other direction. 96 inches converted to feet is 8 feet (96/12 = 8) and 90 inches converted to feet is 7.5 feet (90/12 = 7.5). To calculate area, multiply 8 feet x 7.5 ft and get 60 sq ft.
Another way to do this problem is to figure out the area in the drawing (3.6 inches x 3.84 inches) to get 13.824 sq inches. A scale factor of 25 results in an area scale factor of 25 x 25 (or 625) because area is length times width and each dimension (both length and width) are scaled up by 25. That means you could take the drawing area (13.824 sq inches) and multiply it by the area scale factor of 625 to get 8640 sq inches. Then convert sq inches to sq ft by dividing by 12 twice (or 144) because each length of inches needs to be divided by 12 to convert it to feet. The answer is also 60 sq ft.