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.

Answer 1

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.