Maxima -minima

Let $S$ be a square of unit area. Consider any quadrilateral which has one vertex on each side of S. If $a,b,c$ and $d$ denote the length of the sides of the quadrilateral, then the range of $a^{2}+b^{2}+c^{2}+d^{2}$ is from $[m,n]$ then find $m^{ 2 }+n ^{ 2 }$ .