[ Transfer of side, diagonal, etc.] The Law of Sines

In trapezoid $ABCD (AB \| CD)$, $AB + CD = b$, diagonals $AC$ and $BD$ are related by $5AC = 3BD$. Find the area of the trapezoid if $\angle BAC = 2 \angle DBA$.
Through vertex $C$, draw a line parallel to diagonal $B D$, until it intersects the extension of base $A B$ at point $E$. Then triangle $A C E$ is equal in area to the given trapezoid.

Answer

$\frac{5 \sqrt{11}}{64} b^{2}$.