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2012 AMC 10A Question 21

AMC10 · 2012 AMC 10A

Question 21

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. What is the area of $EFGH?$
  1. $\sqrt{2}$
  2. $\dfrac{2\sqrt{5}}{3}$
  3. $\dfrac{3\sqrt{5}}{4}$
  4. $\sqrt{3}$
  5. $\dfrac{2\sqrt{7}}{3}$