Can you do it using only the height, or distance between opposite sides? In case your wondering: yes, this question does spring from some stupid wargame where the map is broken into hexes. So, in other words, can you tell me how many square kilometers I’ve conquered in my make-believe escapist fantasies? Thanks.
Yes, of course you only need one number. There aren’t different shapes of hexagons - only larger ones and smaller ones.
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 L[sup]2[/sup]/(2 sqrt(3)). You’ve got six of those, so the total area is 3 L[sup]2[/sup]/sqrt(3), or sqrt(3)*L[sup]2[/sup].
Oops, you forgot the area of a triangle is half the base X height.
So the total area is half sqrt(3)*(L squared)
or 0.866 multiplied by (L squared)
You guys, of course, are assuming the OP is referring to a regular hexagon.
Of course, the hexagon is regular, Unc, those board games have lots of roughage.