In trapezoid $A B C D$, the bases $A D=12$ and $B C=8$ are given. On the extension of side $B C$, a point $M$ is chosen such that $C M=2.4$.

In what ratio does the line $A M$ divide the area of trapezoid $A B C D$?
Let segments $A M$ and $C D$ intersect at point $K$. From the similarity of triangles $M K C$ and $A K D$, we find that $C K: K D = C M: A D = 1: 5$.

Therefore, $S_{A K D} = 5 / 6 S_{A C D} = 5 / 6 \cdot 12 / 20 S_{A B C D} = 1 / 2 S_{A B C D}$.

Answer

$1: 1$.