This brain teaser turned out to be a brain boggler. As I am the type of math need that dwells on a single problem until it gas been solved ( and understood ).
I don't think there is enough information given to find the area of shaded region . I tried drawing lines to make congruent pieces of the shaded region in terms of a side of the square call it $x$. I was even attacking it with trig to see if angles given since there are many parallel sides, but still no avail. Please help.