SOLUTION: how i find the area of the regular hexagan

If you are given the regular hexagon:



Draw in all the "spokes":

 

All 6 triangles are congruent equilateral triangles.
Find the area of just the bottom triangle, the green one,
by calculating its height, the red line, by the Pythagorean 
theorem.

 

Then multiply the area of that one triangle by 6,
and you'll have the area of the whole regular hexagon.

Edwin