jmc

Let $a$, $b$, $c$, $d$, $e$, $f$, and $g$ be the lengths shown.



Then $b+d+f+g=12$, and $a+c+e=2+8=10$, so the perimeter of the decagon is $a+b+c+d+e+f+2+g+8+12=12+2+8+12+2+8=\boxed{44}$.