Counting

We can first find the area of a hexagon. If we break it into 6 equilateral triangles, we can calculate their areas. Let's say the side length of the regular hexagon is $s.$ The area of one of the equilateral triangle is $\frac{s^2 \sqrt{3}}{4}$, so the area of the entife hexagon is $\frac{3s^2 \sqrt{3}}{2}.$ Because we know the area is 3, we can solve for s:

$\frac{3s^2 \sqrt{3}}{2} = 3$ ==> $3 s^2 \sqrt{3} = 6$ ==> $s^2 \sqrt{3} = 2$ ==> $3 s^2 = 2 \sqrt{3}$ ==> $s^2 = \frac{2 \sqrt{3}}{3}$

This is best I can go. It get's really complicated if you go even further. Please let me know if I made a mistake.