Let us assume for starters that it is true.
The area of the square is s^2, so that is where you start.
(1 + 2*sqrt(2) ) ^2 = 1 + 4*sqrt(2) + 8 Taking 1 away form that does not leave you with 8.
Let's start again.
If all sides are reduced by 1 , but the square is retained, then the length of the side is 2sqrt(2). Now we have
s^2 = (2sqrt(2) )^2 = 4 * 2 = 8
The question is really not worded clearly enough to give an answer. I think it's true, but the language has to be twisted a bit.
Answer: I'd answer true, but don't be surprised if it is not interpreted the way I did on my second try.