Step 1: Find the full circumference first.
\[ 2\pi r = 2 \times \frac{22}{7} \times 21 = 132 \text{ cm} \]
Step 2: Use the unitary method to get the arc length for 60 degrees.
A full circle is $360^\circ$, so the arc for $60^\circ$ is $\frac{60}{360}$ of the full circumference:
\[ \text{Arc} = 132 \times \frac{60}{360} = 22 \text{ cm} \]
Step 3: Add the two bounding radii.
\[ \text{Perimeter} = 22 + 2(21) = 22 + 42 \]
\[ \boxed{64 \text{ cm}} \]