A convex polygon all of whose vertices have integer coordinates is a convex lattice polygon.
Do there exist mutually non-congruent convex lattice polygons which have the same area and perimeter?
If answer to 1 is yes, are there convex lattice polygons which can be cut into some integer number of convex lattice polygons which are not all congruent and all have same area and perimeter?
Note: The questions have natural analogs in higher dimensions.
