In an equilateral triangle ABC, G is the centroid. Each side of the triangle is 6 cm. The length of AG is:

In Equilateral triangle
$$\eqalign{ & AG:GD = 2:1 \cr & AD = \frac{{\sqrt 3 }}{2}a \cr & AD = \frac{{\sqrt 3 }}{2} \times 6 \cr & AD = 3\sqrt 3 \cr & 3 \to 3\sqrt 3 \cr & 1 \to \sqrt 3 \cr & AG = 2\,{\text{unit}} = 2\sqrt 3 \,{\text{cm}} \cr} $$