$[\mathrm{O}$ The Law of Cosines ] [ The ratio in which the bisector divides the side]

In triangle $A B C$, the bisector of angle $A B C$ intersects side $A C$ at point $K$. It is known that $B C=2, K C=1, B K=$ $\frac{3 \sqrt{2}}{2}$. Find the area of triangle $A B C$.