the scale factor or ratio of two similar figures, will be the same as the ratio of their perimeter, or even the ratio of two corresponding sides.
for example, we have say, an irregular octagon with a perimeter of say 13, and a similar octagon with a perimeter of 39, then
[tex]\bf \cfrac{\textit{small octagon}}{\textit{large octagon}}~\hspace{5em}\cfrac{perimeter}{perimeter}\implies \cfrac{13}{39}\implies \stackrel{simplified}{\cfrac{1}{3}}~\hfill \stackrel{\textit{scale factor}}{1:3}[/tex]
which is another way to say, the smaller is 1/3 of the larger one, or the larger one is 3 times as the smaller one.
