Region closer to one given point than to any other given point

Question

(Q)

*Consider 6 points located at P0=(0,0), P1=(0,4), P2=(4,0), P3=(-2,-2), P4=(3,3), P5=(5,5). Let R be the region consisting of all points in the plane whose distance from P0 is smaller than that from any other Pi; i=1,2,3,4,5. Find the perimeter of the region R.*

I drew a rough sketch from from the conditions given and my answer turns out to be (root(2))*(6+root(5))units, but I am not much sure, as there is no given answer to check.

I need help.

Answer 1

Draw perpendicular bisectors of each $P_0 P_k$ and shade the invalid region (the part that is further from $P_0$ than $P_k$. You would be left with an unshaded valid region whose perimeter goes nicely along grid points. I counted $10$ straight segments and $7$ diagonal segments, but perhaps I counted wrongly.

Answer 2

$P_5$ is too far so doesn't count.
You need to draw mediators between $P_0$ and $P_i$ and you will get a trapezoid with a perimeter equals to $6*(1+1+\sqrt2) - (1+1-\sqrt2) = 10+7\sqrt2$

EDIT : I was wrong so I edited
user21820 is right (if I'm not wrong) :p