I have a polygon (rhombus in this example)
Let's assume we have some arbitrary triangulation for that with N triangles (4 of them here).
The question is the following: having 4 triangles in the first place (see picture below)
can I build a desired shape using them? Move and rotation is allowed (but not scaling). Is there an algorithm or any approach that could help validate this statement?
The only thing I have in mind is to compare areas (sum of triangles and the polygon) but that doesn't give much. Thanks for any suggestion.

