How do you measure a hexagon?
Easiest way (at least for me) to think about it is to notice that a hexagon is made up of six equilateral triangles. You say you know the distance between the two sides of the hexagon; we'll call that L. The height of each triangle is L/2. The triangles have angles of 60 degrees, so the base of each triangle is (L/2) / tan(60) * 2, or L/sqrt(3), because tan(60)=sqrt(3)/2. The area of each triangle is therefore L2/(2 sqrt(3)). You've got six of those, so the total area is 3 L2/sqrt(3), or sqrt(3)*L2.