ABGF is a square with half the perimeter of square ACDE. GD = 5i in. Find the area of the shaded region Round your answer to the nearest tenth.
To find the area of the shaded region, we first need to find the side length of square ACDE.
Let x be the side length of square ACDE.
Since the perimeter of square ABGF is half the perimeter of square ACDE, we can set up the following equation:
4x = 2(4(5i) + 5i)
4x = 8(5i) + 10i
4x = 40i + 10i
4x = 50i
x = 12.5i in
Now, we can find the area of square ACDE:
Area = x^2
Area = (12.5i)^2
Area = 156.25i^2
Next, we can find the area of square ABGF:
Area = (0.5x)^2
Area = (0.5(12.5i))^2
Area = (6.25i)^2
Area = 39.0625i^2
Finally, we can find the area of the shaded region by subtracting the area of square ABGF from the area of square ACDE:
Shaded Area = 156.25i^2 - 39.0625i^2
Shaded Area = 117.1875i^2
Rounded to the nearest tenth, the area of the shaded region is 117.2 square inches.