A "lattice triangle" is a triangle in the rectangular plane whose three vertices have integer x- and y-coordinates. In this presentation we will discuss and answer some fundamental questions regarding the areas of such triangles.

* Which numbers A arise as the area of a lattice triangle?

* For given area A, how many non-congruent lattice triangles have area A?

* For a given area A can we find a procedure to construct all lattice triangles with area A?

The last of these questions is the trickiest one. To answer it we will describe and examine an elementary method that transforms one lattice triangle into another
lattice triangle with the same area.