ABGF is a square with half the perimeter of square ACDE. GD=5 in. Find the area of the shaded region. Round your answer to the nearest tenth. Please show all work in order to receive full credit. Either type it out or you may use the symbol to upload a picture of your work.
First, let's find the perimeter of square ACDE. Since ABGF is a square with half the perimeter of ACDE, the perimeter of ABGF is 20 inches. This means the perimeter of ACDE is 40 inches.
Since all sides of a square are equal, each side of ACDE is 40/4 = 10 inches.
Now, let's find the area of square ACDE. The area of a square is side squared, so the area of ACDE is 10^2 = 100 square inches.
Now, let's find the area of the shaded region. Since GD=5 inches, each side of ABGF is 5 inches. The area of ABGF is 5^2 = 25 square inches.
Finally, the area of the shaded region is the difference between the area of ACDE and the area of ABGF: 100 - 25 = 75 square inches.
Therefore, the area of the shaded region is 75 square inches.