Find $ S1$ in the parallelogram below

geometry euclidean-geometry plane-geometry

Solution 1:

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.

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