How large is the distance between centroids of two equilateral triangles

Question

I have a problem. I have a triangle grid with a lot of equilateral triangles. Now I want to know what the distance is between two centroids. How can I do that?

Here is a sample image of the grid:triangle grid

Answer 1

Can you work out the perpendicular height of your triangles?

The distance from the base of a triangle to its centroid if $h \over 3$, where $h$ is the perpendicular height of the triangle.

The distance between two centroids is then this distance doubled.

Answer 2

Supposing the grid length is 1 unit, we know the distance from the centroid to a side is $\frac{1}{2\sqrt{3}}$ units. Thus the distance between two neighbouring centroids is $\frac{1}{\sqrt{3}}$. For centroids that are further apart, note that the centroids form a hexagonal grid; computation from here is not too difficult.