Square pyramid $ABCDE$ has base $ABCD$, which measures $4$ cm on a side, and altitude $\overline{AE}$ perpendicular to the base, which measures $8$ cm. Point $P$ lies on $\overline{BE}$, one fourth of the way from $B$ to $E$. Point $Q$ lies on $\overline{DE}$, one fourth of the way from $D$ to $E$, and point $R$ lies on $\overline{CE}$, three fourths of the way from $C$ to $E$. What is the area, in square centimeters, of $△PQR$?