Question

ABGF is a square with half the perimeter of square ACDE. GD = 4 in. Find the area of the shaded region. The shaded area is FGBCDE.

I kinda know what needs to happen, but I'm lost and confused on the steps to get there:/ Step by step would be most helpful:) Thank you

Answer 1

No idea where CDE are in relation to BGF. All you have said is that the two squares share corner A.

However, you do know that the smaller square has sides 1/2 as long as the larger one, so its area is 1/4 as big.

I suspect you can use that to determine the shaded area.

Also, a square's diagonal is √2 as long as its sides.

Answer 2

What did you end up getting I am very stuck.

Answer 3

(Like a somewhat continuation of Steve's post)
A square's diagonal is √2 as long as it's sides, so sides ED, DC, CA, and AE all equal 4√2.

Okay so we know that the area formula is base*height, so that would make it:
4 root 2 * 4 root 2, which equals 32in^2. So now you have the area of the entire square.

We know that smaller square has sides 1/2 as long as the larger one, so its area is 1/4 as big (thanks Steve). Therefore, to get the area of the smaller square you do 32*1/4. That equals 8in^2.

Some simple subtraction (32in^2-8in^2=24in^)

The area of the shaded region is 24in^2 ^w^