Let points $A$ = $(0 ,0 ,0)$, $B$ = $(1, 0, 0)$, $C$ = $(0, 2, 0)$, and $D$ = $(0, 0, 3)$. Points $E$, $F$, $G$, and $H$ are midpoints of line segments $\overline{BD},\text{ }  \overline{AB}, \text{ } \overline {AC},$ and $\overline{DC}$ respectively. Find the area of quadrilateral $EFGH$. The original answer is in the form \frac{k\sqrt{m}}{n}, please give the value of k + m + n.

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