How to get the shaded region of the rectangle? I have this problem:

So my development was:
Denote side of rectangle with: $2a, 2b$. 
So, $4ab= 64, ab = 16$
Denote shaded region with $S$
Denote area of triangle $DGH = A_1$ and triangle $FBE = A_2$.
So, $A_1 + A_2 + S = 64$
$S = 64 - A_1 - A_2$
The triangles $A_1, A_2$ are congruent because $LAL$ congruence criterion.
The area of $A_1$ and $A_2$, is the same and i got it with this way:
Since, the $\angle{GDH} = 90$ and the median from this angle to the base $HG$, that is the altitude of the triangle $DGH$,  will measure the half of the $HG$ side.
And the $HG$ side by Pythagorean theorem, will be $\sqrt{a^2 + b^2}$, that will be the base of the triangle.
And the altitude will be: $\frac{\sqrt{a^2 + b^2}}{2} $,
So the Area of $A_1 = \frac{a^2 + b^2}{4}$
So, $A_1 + A_2 = \frac{a^2 + b^2}{2}$
Then, $64 - (\frac{a^2 + b^2}{2}) = S$
And, $-(a^2 - 8ab + b^2) = 2S$
And I have not been able to continue from here, what should I do? Thanks in advance.

Hint:



*

*there are eight small red triangles all with the same area 

*six of them are shaded
