Centre of gravity and centroid

For any triangle, both are at the average coordinates of the three vertices: $(a+b+c)/3$. This holds true for a triangle of uniform density. And I am interpreting "center of gravity" as described here.

The both coordinates(COM&CG) of a plane surface of uniform mass density in uniform gravitational field are same.

Centre of Gravity and Centre of mass of a body on surface of earth are same. But, the centroid depends on the dimensions of the body(triangle) but not on mass. Hence for a non uniform mass distribution the centroid doesn't coincide with Centre of Gravity.