Dear Sreinivas
I tried your corrected solution too.
It simply does not work.
What it does is - divides the white space into two equal halves.
Anything beyond this produces 4 pieces which are asymetrical, un-identical and do not appear to have the same area.
Please illustrate with diagram your solution - if you think you have got it right.
Now, consider my solutions :
I have two solutions which produce four equal areas, but they are not symmetrical in shape.
(1) The first solution involves dividing the white space into three equal squares (as apparent prima facie); then divide each small square into 4 smaller squares, making total 12 smaller squares.
icking up any 3 adjacent squares (other than those used in the original solution) will give 4 shapes, each made out of 3 smallest squares .
(2) The second solution i similar, buthere you divide each small squares into 4 equal triangles -equilateral - by joining the diagonals of the smaller square.
You will get 12 small triangles, out of which you need to pick sets of 3; thus totaling 4 sets of equal triangles and hence 4 equal areas.
Remember, in both the solutions, the areas are equal but the shapes are not identical.
Regards.