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.
To find the area of the shaded region, we first need to find the perimeter of square ACDE.
Let x be the side length of square ACDE. Since ABGF is a square with half the perimeter of ACDE, the side length of ABGF is x/2.
Perimeter of ACDE = 4x
Perimeter of ABGF = 2x
Given that GD = 5 in, and GD is the same as half the side of ABGF, we can set up the following equation:
x/4 = 5
x = 20
The side length of square ACDE is 20 in, and the side length of square ABGF is 10 in.
To find the area of the shaded region, we need to subtract the area of square ABGF from the area of square ACDE:
Area of square ACDE = (20 in)^2 = 400 sq in
Area of square ABGF = (10 in)^2 = 100 sq in
Area of shaded region = 400 sq in - 100 sq in = 300 sq in
Therefore, the area of the shaded region is 300 square inches.