smc

The two straight sides of the "monster" are radii of length $1$ cm, so their total length is $1+1=2$ cm. The circular arc forms $\frac{360^{\circ }-60^{\circ }}{360^{\circ }}=\frac{5}{6}$ of the entire circle, and a circle with radius $1$ cm has circumference $2\pi (1)=2\pi$ cm, so the length of the arc is $\left(\frac{5}{6}\right)(2\pi )=\frac{5}{3}\pi$ cm. Hence the total perimeter in cm is $\boxed{\frac{5}{3}\pi +2}$.