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2019 AMC 12B Question 18

AMC12 · 2019 AMC 12B

Question 18

Square pyramid $ABCDE$ has base $ABCD,$ which measures $3$ cm on a side, and altitude $\overline{AE}$ perpendicular to the base, which measures $6$ cm. Point $P$ lies on $\overline{BE},$ one third of the way from $B$ to $E;$ point $Q$ lies on $\overline{DE},$ one third of the way from $D$ to $E;$ and point $R$ lies on $\overline{CE},$ two thirds of the way from $C$ to $E.$ What is the area, in square centimeters, of $\triangle PQR?$
  1. $\dfrac{3\sqrt2}{2}$
  2. $\dfrac{3\sqrt3}{2}$
  3. $2\sqrt2$
  4. $2\sqrt3$
  5. $3\sqrt2$