ABGF is a square with half the perimeter of square ACDE. GD = 5 in. Find the area of the shaded region. The shaded area is FGBCDE.
Let x be the side length of square ABGF. Since ABGF is half the perimeter of square ACDE, we have:
4x = 2(8x) = 16x
Solving for x, we get x = 2 in.
Now, since GD = 5 in and AG = 2 in, we can find the length of AD using the Pythagorean theorem:
AD = sqrt(AG^2 + GD^2) = sqrt(2^2 + 5^2) = sqrt(29) in.
The area of the shaded region FGBCDE is equal to the area of square ACDE minus the area of square ABGF:
Area(FGBCDE) = Area(ACDE) - Area(ABGF)
= AD^2 - x^2
= (sqrt(29))^2 - (2)^2
= 29 - 4
= 25 in^2
Therefore, the area of the shaded region FGBCDE is 25 square inches.