Question 1066704
The number of sides of a polygon using the number of diagonals is,
{{{D=S(S-3)/2}}}
{{{9=S(S-3)/2}}}
{{{S^2-3S=18}}}
{{{S^2-3S-18=0}}}
{{{(S-6)(S+3)=0}}}
{{{S-6=0}}}
{{{S=6}}}
So it's a hexagon.

{{{A[HEX]= (3/2)sqrt(3)X^2}}}
{{{(3/2)sqrt(3)X^2=196sqrt(3)}}}
{{{X^2=392/3}}}
{{{X=sqrt(392/3)}}}
{{{X=(14/3)sqrt(6)}}}
So the perimeter is then,
{{{P=6X}}}
{{{P=28sqrt(6)}}}{{{cm}}}