Challenge Level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

Can you draw triangles of area 1, 2, 3, ... square units?

Can you draw a triangle with an area of 1.5 square units?

What is the area of the smallest triangle you can draw? Is this triangle unique?

How many triangles of of area 2 square units can you draw and can you create "families" or "groups" of these triangles?