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

Question

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!!

score 2 · Accepted Answer · answered Aug 18 '17 at 05:17

2

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

answered Aug 18 '17 at 05:17

dxiv

76,497

So what is the usage of $S_{BPC}$? – Hamid Reza Ebrahimi Aug 18 '17 at 05:22
@HamidRezaEbrahimi $S_{BPC}$ is not used or needed, unless you want to determine $S_{APD}$ too. – dxiv Aug 18 '17 at 05:24

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

1 Answers1