The circumference of a circle is 22 cm.

Let the radius of the circle be r.
​Now,

Circumference $=22$

$\Rightarrow 2 \pi r=22$

$\Rightarrow r=\frac{22 \times 7}{44}=\frac{7}{2} \mathrm{~cm}$

Now, Area of quadrant $=\frac{1}{4} \pi r^{2}=\frac{1}{4} \times \frac{22}{7} \times\left(\frac{7}{2}\right)^{2}=\frac{77}{8} \mathrm{~cm}^{2}$

Hence, the area of the quadrant of the circle is $\frac{77}{8} \mathrm{~cm}^{2}$.