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2012 AMC 10A Problem 21

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2012 AMC 10A Problem 21AMC 10 Step by Step

Name: Date: September 13, 2026

Coordinate Geometry · difficulty 3 of 5 · about 5 min · position P21-25

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 $EFGH$ ?

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

2012 AMC 10A Problem 21

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