ABGF is a square with half the perimeter of square ACDE. GD=4 in. . Find the area of the shaded region. (3 points)
To find the area of the shaded region, we first need to find the side length of square ACDE.
Since square ABGF has half the perimeter of square ACDE, we can set up the following equation:
Perimeter of ABGF = 2(AB + BG) = Perimeter of ACDE = 4(AD)
Let x be the side length of square ACDE.
Then, x/2 is the side length of square ABGF.
2(x/2 + x/2) = 4x
x = 4
So, the side length of square ACDE is 4 inches.
Now, the area of square ACDE is x^2 = 4^2 = 16 square inches.
The area of the shaded region is the area of square ACDE minus the area of square ABGF:
Area of shaded region = 16 - (4^2)/2 = 16 - 8 = 8 square inches
Therefore, the area of the shaded region is 8 square inches.