Pretty self explanatory.
If I have a quadrilateral, I'm pretty sure I can't place 3 dots randomly on the quadrilateral in any position and claim that the area contained by these dots is equal to the area of the quadrilateral. I think this applies to polygons with more sides too.
I may be wrong, but if this is true, does this concept have a name? If not, does it need to be proven- how would I do that?
Edit: I forgot to mention, but as pointed out this does not apply to convex polygons- can it be proven for concave polygons?