What is the perimeter, in cm, of quadrilateral $ABCD$ if $\overline{AB} \perp \overline{BC}$, $\overline{DC} \perp \overline{BC}$, $AB=9$ cm, $DC=4$ cm, and $BC=12$ cm?
(9-4)^2+12^2=13^2
13+12+9+4=$\boxed{38}$
+502 
