In the triangle $ABC$, point $D$ is given on the extension of side $CA$ beyond $A$, and point $E$ is given on the extension of side $CB$ beyond $B$, such that $AB = AD = BE$. The angle bisectors from $A$ and $B$ of triangle $ABC$ intersect the opposite sides at points $A_1$ and $B_1$, respectively. What is the area of triangle $ABC$ if the area of triangle $DCE$ is 9 units, and the area of triangle $A_1CB_1$ is 4 units?