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the area can also be expressed in terms of the apothem a and the perimeter p. For the regular hexagon these are given by a = r, and p, so
:

The regular hexagon fills the fraction of its circumscribed circle.

If a regular hexagon has successive vertices A, B, C, D, E, F and if P is any point on the circumcircle between B and C, then PE + PF {{= PA + PB + PC + PD}}.

It follows from the ratio of circumradius

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