Answer
$22$ inches.
Work Step by Step
This figure has 8 sides, and the length of 2 sides are missing. The sides that are given are of length $2,1,2,1,4,$ and $5$ inches. According to the figure, the side with the length not given at the top is $2$ less than the base, which has length $5$ inches, so the side length of that side is $3$ inches. Also, the other side length missing has to be the height of the figure ($6$) minus $2$. The other side length is $4$ inches. Add all the sides.
$$2+1+2+1+4+5+3+4 =\boxed{22} in. $$
