Final answer:
The area of the larger square is 64 square inches, while the smaller square is 16 square inches, giving a ratio of 4:1. This shows that the larger square's area is 4 times that of the smaller square, illustrating that area ratios of similar figures are the square of the scale factor.
Step-by-step explanation:
The question asks us to compare the area of a larger square to the area of a smaller square where the dimensions of the larger square are twice those of the smaller one. To find the area of a square, you multiply the length of one side by itself, which is represented as side length squared (s²). If the side length of the smaller square is 4 inches, then its area is 4² or 16 square inches. The larger square has a side length of 8 inches (twice the smaller), so its area is 8² or 64 square inches.
When comparing the two areas, we find that the area of the larger square is 64 square inches and the smaller square is 16 square inches, which gives us a ratio of 64:16 or 4:1. Therefore, the area of the larger square is 4 times larger than the area of the smaller square. This demonstrates the rule that the ratio of areas of similar figures is the square of the scale factor.