A hexagon does not have a radius. A circumscribed circle has a radius equal to the measure of the segment joining the center of the hexagon with one of its vertices. If that is what you meant:
A regular hexagon is composed of 6 congruent equilateral triangles. Two of the sides of each of these triangles are circumcircle radii as described above and the third side is one of the sides of the hexagon. Since these are equilateral triangles, all three sides are of equal measure. Hence, the circumcircle radius is equal in measure to the measure of a side of a regular hexagon.
The area of a regular hexagon given the measure of a side, , is given by:
