Question 1205543
<br>
When the side length of the regular hexagon is 1, the distance between parallel sides of the hexagon is NOT 2/sqrt(3).<br>
The distance, as you have found, is 2(sqrt(3)/2) = sqrt(3).<br>
Picture the regular hexagon as being composed of 6 equilateral triangles.<br>
Draw a line connecting opposite sides of the hexagon, dividing 2 of those equilateral triangles each into two 30-60-90 right triangles.  In those right triangles, the short leg is 1/2, so the long leg is sqrt(3)/2; and the distance between the opposite sides of the hexagon is twice that, which is sqrt(3).<br>