Final answer:
The area of the larger square with a side length of 8 inches is 64 square inches, which is four times the area of the smaller square with a side length of 4 inches.
Step-by-step explanation:
The area of a square is calculated as the side length squared. If Marta has one square with a side length of 4 inches, the area of that square is 16 square inches (4 inches × 4 inches). When she has another square whose dimensions are twice as large as the first square, its side length is 8 inches.
The area of the larger square is 64 square inches (8 inches × 8 inches), which is exactly four times the area of the smaller square since the area of a square scales with the square of its side length.
In the given figure, points A, B, C, and D form a square. Points E and F are the midpoints of sides AB and CD, respectively. To find the area of square ABCD, we can use the formula for the area of a square: area = side^2.
Since AD and BC are the sides of the square, we can find their lengths by using the distance formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).
Once we have the lengths of the sides, we can calculate the area of the square by squaring one of the side lengths.