Problem 333

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Problem 333: (2019 AMC 12b, 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 $\triangle PQR?$

$\textbf{(A) } \frac{3\sqrt2}{2} \qquad$ $\textbf{(B) } \frac{3\sqrt3}{2} \qquad$ $\textbf{(C) } 2\sqrt2 \qquad$ $\textbf{(D) } 2\sqrt3 \qquad$ $\textbf{(E) } 3\sqrt2$

Solution

Exercise 333: Solution

Square pyramid $ABCDE$ has base $ABCD$ with side length $3$ cm and altitude $\overline{AE}$ perpendicular to the base with $AE=12$ 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 $E$; point $R$ lies on $\overline{CE}$, halfway from $C$ to $E$. What is the area of $\triangle PQR$, in square centimeters?

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