In triangle $PQR$, angle $Q$ is a right angle, the measure of angle $R$ is $40^{\circ }$, and the length of $\overline{QR}$ is 20 units. If the area, in square units, of triangle $PQR$ can be represented by the expression $k\tan 40^{\circ }$, where $k$ is a constant, what is the value of $k$?