The hexagon is effectively made up of triangles of strands, each side has 5 strands therefore the triangle would be the 5 strands the 4 underneath that, then 3 and 2 under that and then finally the one in the middle.
This is basically triangular numbers which the nth term is n(n+1)/2... because there are 6 'triangles' the nth term would be 6n(n+1)/2.... however this includes the strands that are counted twice, e.g each side shares 2 strands with other sides. Therefore the amount of strands shared is equal to 6(n-1)+5, this is because there is 6 lines of strands that are shared in between each side. And the center shares its strand with all of the sides, so we do (n-1)... and the center shares 6 therefore we +5. (not 6 because we still need to count it as one strand).
So now the nth term is 6n(n+1)/2 - (6(n-1)+5)
we simplify this so (6n^2+6n)/2 - (6n-6+5)
3n^2+3n-6n+1
therefore the nth term is 3n^2-3n+1...
size n = 3n^2-3n+1
size 10 = 271 strands