jmc

We have $\angle K=180^{\circ }-90^{\circ }-60^{\circ }=30^{\circ }$, so $JKL$ is a 30-60-90 triangle. Since $\overline{JL}$ is opposite the $30^{\circ }$ angle, we have $JL=KL/2=10$. Since $\overline{JK}$ is opposite the $60^{\circ }$ angle, we have $JK=JL\sqrt{3}=10\sqrt{3}$. Therefore, $$[JKL]=\frac{(JK)(JL)}{2}=\frac{(10\sqrt{3})(10)}{2}=\boxed{50\sqrt{3}}.$$