Find $S_{PCD}$ given $S_{ABCD},S_{ABP},S_{BPC}$

In the following figure,$ABCD$ is a paralleogram in which point $P$ lies in triangle $ABD$ and the areas of $ABCD,ABP,BPC$ are known to be $s_1,s_2,s_3$ respectively. Find $S_{PCD}$

I think the number of unknowns in this problem is more than the number of equations that can be formed!!

$S_{ABP}+S_{PCD}=\frac{1}{2}PE\cdot AB+\frac{1}{2}PF\cdot CD=\frac{1}{2}(PE+PF)\cdot AB=\frac{1}{2}EF\cdot AB=\frac{1}{2}S_{ABCD}$
• So what is the usage of $S_{BPC}$? – Hamid Reza Ebrahimi Aug 18 '17 at 5:22
• @HamidRezaEbrahimi $S_{BPC}$ is not used or needed, unless you want to determine $S_{APD}$ too. – dxiv Aug 18 '17 at 5:24