Final answer:
The area of the larger square is 4 times larger than that of the smaller square because the side lengths are scaled by a factor of 2, which when squared, gives the area scale factor.
Step-by-step explanation:
The area of a square is calculated by squaring its side length. If Marta has a square with a side of 4 inches, the larger square will have sides of 4 inches × 2, which is 8 inches. Hence, the area of the larger square is 8 inches × 8 inches = 64 square inches. To understand how this compares to the smaller square's area:
- Smaller square area: 4 inches × 4 inches = 16 square inches
- Larger square area: 64 square inches
Therefore, the area of the larger square is 64 square inches / 16 square inches = 4, which means it is 4 times larger than the area of the smaller square. This illustrates the rule that the ratio of areas of similar figures is the square of the scale factor.