Question

The length of a side of a square is 1 . The midpoints of the sides of the square are combined, resulting in a smaller square. The center points of the new square are connected again to form a square"

Answer 1

The area of a square with side lengths doubled is four times the area of the original square, resulting in a 4 to 1 ratio in areas.

Step-by-step explanation:

The question involves comparing the areas of two squares, where one square has dimensions that are doubled compared to the other square. The side length of the larger square would be calculated as 4 inches x 2, resulting in 8 inches. To compare the areas of the two squares, we can write a ratio: the area of the smaller square is 16 square inches (4 inches × 4 inches), and the area of the larger square is 64 square inches (8 inches × 8 inches). The ratio of the larger area to the smaller area is 64 to 16, which simplifies to 4 to 1. Hence, the area of the larger square is four times that of the smaller square.