Final answer:
Kevin is correct; the area of a square can be found by squaring its side length. With Marta’s squares, the area of the larger one, with sides twice as long as the smaller one, is four times greater due to the square of the scale factor.
Step-by-step explanation:
Kevin is indeed correct when he says that to find the area of a square, you can multiply the length of one side by itself. This method is a fundamental principle in geometry. If a square has a side of length a, then its area is a multiplied by a, which is written as a².
When comparing two squares where one square has side lengths that are double those of the smaller square, the area of the larger square is four times greater. This is because the area is proportional to the square of the scale factor. For instance, with Marta's squares, the first square has a side length of 4 inches, making the area 16 square inches. The second square has a side length of 8 inches (4 inches × 2), so its area becomes 64 square inches, which is 4 times larger than that of the first square.
This principle extends beyond just squares. When we discuss similar geometric shapes, the ratio of their areas is always the square of the ratio of their corresponding lengths.