Where do all your added numbers come from?
I know what the answer is. I answered first.
But neither of you 2 has said where any of your numbers come from.
Oh I get it.
You both arbitrarily chose angle AEG to be 90 degrees AND angle EGB=45 degrees.
And you arbitrarily chose AB to equal AD
Only you didn't bother to explain that is what you were doing.
This does make it easier,
You do not need to approximate anything though.
If you let AB=x units and CF=h units then
it is easy to work out that h=sqrt6, and x=sqrt(8/3)
And then that blue area = 8 units squared.