The circumference of a circle is 8 cm.

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

Circumference $=8$

$\Rightarrow 2 \pi r=8$

$\Rightarrow r=\frac{14}{11} \mathrm{~cm}$

We have $r=\frac{14}{11} \mathrm{~cm}$ and $\theta=72^{\circ}$

Area of sector $=\frac{\theta}{360^{\circ}} \times \pi r^{2}=\frac{72^{\circ}}{360^{\circ}} \times \frac{22}{7} \times\left(\frac{14}{11}\right)^{2}=1.02 \mathrm{~cm}^{2}$

Hence, the area of the sector of the circle is 1.02 cm2.

Disclaimer : If we take the circumference of the circle is 8 cm then the area of the sector will be 1.02 cm2. But if we take the circumference of the circle is 88 cm then the area of the sector will be 123.2 cm2