Final answer:
The ratio of areas of similar geometric figures is the square of the scale factor. So, the area of the larger square, with its side length being twice that of the smaller square, is 4 times greater than that of the smaller square.
Step-by-step explanation:
The question revolves around the concept that the ratio of areas of similar geometric figures is equal to the square of the scale factor of their corresponding side lengths. We know that the side length of the larger square is twice that of the smaller square. Given this information, if the side length of the smaller square is 4 inches, then the side length of the larger square is 4 inches x 2 = 8 inches. Since the scale factor is 2 (the larger square's side length is twice as big as the smaller one's), the ratio of the areas is 2², which equals 4. Therefore, the area of the larger square is 4 times larger than the area of the smaller square.
When comparing the areas of these squares directly through a proportion, the area of the larger square (with a side length of 8 inches) is 8 inches x 8 inches = 64 square inches. The area of the smaller square (with a side length of 4 inches) is 4 inches x 4 inches = 16 square inches. Thus, confirming, the area of the larger square is indeed 4 times the area of the smaller square.