Each point in the hexagonal lattice shown is one unit from its nearest neighbor. How many equilateral triangles have all three vertices in the lattice?
Sadly, there isn't much to do other than count them one by one.
There are 9 one unit triangles.
There are 3 two unit triangles.
There are 1 three unit triangles.
9 + 3 + 1 = 13
I hope this helped. :))