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.%C2%A0 Please show all work in order to receive full credit. Either type it out or you may use the%C2%A0%C2%A0symbol to upload a picture of your work.
First, let's find the perimeter of square ACDE. Since ABGF has half the perimeter of ACDE, we can set up the following equation:
Perimeter of ABGF = 0.5 * Perimeter of ACDE
4 + 4 + 4 + 4 = 0.5 * (x + x + x + x)
16 = 0.5 * 4x
16 = 2x
x = 8 in
Now, we can find the area of square ACDE:
Area of ACDE = side * side
Area of ACDE = 8 * 8
Area of ACDE = 64 sq in
Now, we need to find the area of the shaded region. The area of the shaded region is the area of square ACDE minus the area of square ABGF. Since ABGF has half the side length of ACDE, we can find the area of square ABGF by dividing the area of square ACDE by 4:
Area of ABGF = Area of ACDE / 4
Area of ABGF = 64 / 4
Area of ABGF = 16 sq in
Now, we can find the area of the shaded region:
Area of shaded region = Area of ACDE - Area of ABGF
Area of shaded region = 64 - 16
Area of shaded region = 48 sq in
Therefore, the area of the shaded region is 48 square inches.