\(19.4 \mathrm{~cm}\)
The perimeter of a sector is the sum of the length of the arc and the two radii of the circle i.e.
\(P=l+2 r\)
where \(l=\frac{\theta}{360} \times 2 \pi r\)
\begin{aligned}
l &=\frac{150}{360} \times 2 \times \frac{22}{7} \times 4.2 \\
l &=\frac{150}{360} \times 2 \times \frac{22}{7} \times 4.2 \\
l &=\frac{27,720}{2520}=11 \mathrm{~cm} \\
& \therefore p=2 \times 4.2+11=19.4 \mathrm{~cm}
\end{aligned}