In right triangle $ABC$, angle $B$ is the right angle, the measure of angle $C$ is $45^{\circ }$, and the length of $\overline{BC}$ is 10 units. If the area, in square units, of triangle $ABC$ can be represented by the expression $k\tan 45^{\circ }$, where $k$ is a constant, what is the value of $k$?