My doubt is about how you obtain the Euler characteristic of this polygon with hole.
It has $6$ vertices, $6$ edges and $1$ face, so $6+1-6=1$.
But if you triangulated it using $3$ parallelograms, you get $6$ vertices, $3$ faces, $9$ edges, so it is zero.
How is it possible? (Euler characteristic is an invariant.)
Thanks in advance!