Geometry

mmm...take a look at the points given. 

$P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1$

This is essentially just the perimeter of the decagon $P_1P_2P_3P_4P_5...P_{10}$

The lenngth of one side is essentially

$radius/2 ( -1 +\sqrt 5)$

Now that we know one side, we can find the perimeter through the equation

$10 (1/2) ( -1 + \sqrt 5) = 5 ( -1 + \sqrt 5) ≈ 6.18$

Thus, the answer is 6.18, 

Thanks! :)