Computing the lengths of the obtained trapezium $ABCD$ is a quadrilateral. A line through $D$ parallel to $AC$ meets $BC$ produced at $P$. My book asked me to show that the area of $APB$ and $ABCD$, are the same, which I did. But it aroused my interest. So I researched on how do we compute the sides or simply characterize the trapezium $ACPD$, if we know the sides and angles of $ABCD$. But I was not able to find any result. Please help.

Edit：

It is easy find all for $ACPD$, $AC$ is trivial to get. then you can have $F$, since $AB$ is known,so $AF,FB,FC$ can be obtained. then you can find $CP,DP$ since $AC$  \\  $DP$
