KöMaL 2014 C1260

The midpoints of sides $AB$ , $BC$ , $CD$ , $DA$ of a unit square $ABCD$ are $E$ , $F$ , $I$ , $H$ , respectively. Let $M$ denote the intersection of the lines $ED$ and $HI$ , and let $G$ denote the intersection of the lines $EC$ and $FI$ . Find the area of the quadrilateral $MEGI$ .