In the figure below, $abcd$ is a square piece of paper 6 cm on each side. corner $c$ is folded over so that it coincides with $e$, the midpoint of $\overline{ad}$. if $\overline{gf}$ represents the crease created by the fold such that $f$ is on $cd,$ what is the length of $\overline{fd}$? express your answer as a common fraction.