Two circles $S_1$ and $S_2$, with radii $6$ units and $3$ units respectively, are tangent to each other externally. Let $AC$ and $BD$ be their direct common tangents, with $A$ and $B$ on $S_1$, and $C$ and $D$ on $S_2$. Find the area of quadrilateral $ABDC$ to the nearest integer.

Let's think step by step and output the final answer within \boxed{}.
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