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

Answer: Option C

In Equilateral triangle
$$\begin{array}{rl}& AG:GD=2:1\\ & AD=\frac{\sqrt{3}}{2}a\\ & AD=\frac{\sqrt{3}}{2}\times 6\\ & AD=3\sqrt{3}\\ & 3\to 3\sqrt{3}\\ & 1\to \sqrt{3}\\ & AG=2\text{unit}=2\sqrt{3}\text{cm}\end{array}$$