#### Answer

P=40$\sqrt 3$

#### Work Step by Step

In a regular hexagon, the length of the radius of a circle inscribed within it is equal to an apothem. The apothem of a regular hexagon is the long leg of a 30 60 90 triangle with half of a side as the short leg. Therefore:
.5s=$\frac{a}{\sqrt 3}$
s=$\frac{20\sqrt 3}{3}$
P=6s
P=6($\frac{20\sqrt 3}{3}$)
P=40$\sqrt 3$