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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!! enter image description here

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$S_{ABP}+S_{PCD}=\frac{1}{2}PE\cdot AB+\frac{1}{2}PF\cdot CD=\frac{1}{2}(PE+PF)\cdot AB=\frac{1}{2}EF\cdot AB=\frac{1}{2}S_{ABCD}$

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  • $\begingroup$ So what is the usage of $S_{BPC}$? $\endgroup$ – Hamid Reza Ebrahimi Aug 18 '17 at 5:22
  • $\begingroup$ @HamidRezaEbrahimi $S_{BPC}$ is not used or needed, unless you want to determine $S_{APD}$ too. $\endgroup$ – dxiv Aug 18 '17 at 5:24

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