area of regular polygon = 1/2*apothem*perimeter
so 500 = 1/2 *apothem*perimeter
1000 = apothem * perimeter
perimeter of hexagon is 6 bases and apothem is sqrroot(3)/2*base
1000 = sqrroot(3)/2 *b*6b
1000 = 3sqroot(3) * b^2
so b^2 = 1000/3sqroot(3) or b^2 = 1000sqroot(3)/9
or b = sqroot [1000sqroot(3)] / 3
then b (radius) is approximately 13.87