Points $M,N,P,Q$ are taken on the sides $AB,BC,CD,DA$ respectively of a square $ABCD$ such that $AM=BN=CP=DQ=\frac1nAB$. Find the ratio of the area of the square determined by the lines $MN,NP,PQ,QM$ to the ratio of $ABCD$.
Source: Slovenia 1997 2nd Grade P2
Tags: geometry
Points $M,N,P,Q$ are taken on the sides $AB,BC,CD,DA$ respectively of a square $ABCD$ such that $AM=BN=CP=DQ=\frac1nAB$. Find the ratio of the area of the square determined by the lines $MN,NP,PQ,QM$ to the ratio of $ABCD$.