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2012 AMC 10A Problems/Problem 21

Revision as of 21:56, 8 February 2012 by Ace316 (talk | contribs) (Created page with "==Problem 21== Let points <math>A</math> = <math>(0 ,0 ,0)</math>, <math>B</math> = <math>(1, 0, 0)</math>, <math>C</math> = <math>(0, 2, 0)</math>, and <math>D</math> = <math>(...")
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Problem 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 $EFGH$?

$\textbf{(A)}\ \sqrt{2}\qquad\textbf{(B)}\ \frac{2\sqrt{5}}{3}\qquad\textbf{(C)}\ \frac{3\sqrt{5}}{4}\qquad\textbf{(D)}\ \sqrt{3}\qquad\textbf{(E)}\ \frac{2\sqrt{7}}{3}$

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