A rectangular piece of paper $ABCD$ is folded so that edge $\overline{CD}$ lies along edge $\overline{AD},$ making a crease $\overline{DP}.$ The crease is unfolded, and then the paper is folded again so that edge $\overline{AB}$ lies along edge $\overline{AD},$ making a second crease $\overline{AQ}.$ The two creases meet at $R,$ forming triangles $PQR$ and $ADR$. If $AB=5\mbox{ cm}$ and $AD=8\mbox{ cm},$ what is the area of quadrilateral $DRQC,$ in $\mbox{cm}^2?$
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