ksf-2015-st-27

In the rectangle \(ABCD\) shown in the figure, \(M_1\) is the midpoint of \(DC\), \(M_2\) is the midpoint of \(AM_1\), \(M_3\) is the midpoint of \(BM_2\) and \(M_4\) is the midpoint of \(CM_3\).

Question:

Find the ratio between the areas of the quadrilateral \(M_1M_2M_3M_4\) and of the rectangle \(ABCD\).