For reference:
In the picture; if $ABCD$ is a parallelogram; $S3 = 10\,\text{m}^2$ and $S2 = 3\,\text{m}^2$. Calculate $S1$ (Answer: $7\,\text{m}^2$) My picture was wrong...I put the right one now...I'm sorry for the mistake
My progress:
$S3 = S_{AB} =S_{AGC}=S_{AGB}= 10$
$S1 = \dfrac{S3+S_{GHD}}{2}=\dfrac{BD\cdot h}{2}$
$\dfrac{S_{CGI}}{S_{CIA}}=\dfrac{GI}{AI}$
$\dfrac{3}{S_{OID}}=\dfrac{AI}{ID}$
$S_{OAC} = \dfrac{AC\cdot r}{2}$
....???
It is easy to see that $S_{BOC} + S_{AOD}$ is equal to half the area of the parallelogram.
On the other hand, $S_{ACD}$ is clearly also equal to half the area of the parallelogram.
Taking out their intersection, we get $S_1 + S_2 = S_3$.
The circle is for decoration.