In a circle of radius 10.5 cm, the minor arc is one-fifth of the major arc

Let the length of the major arc be $x \mathrm{~cm}$

Radius of the circle = 10.5 cm

$\therefore$ Length of the minor $\operatorname{arc}=\frac{x}{5} \mathrm{~cm}$

Circumference $=\left(x+\frac{x}{5}\right)=\frac{6 x}{5} \mathrm{~cm}$

Using the given data, we get:

$\frac{6 x}{5}=2 \times \frac{22}{7} \times \frac{21}{2}$

$\Rightarrow \frac{6 x}{5}=66$

$\mathrm{Or}$

$x=55$

$\therefore$ Area of the sector corresponding to the major arc $=\left(\frac{1}{2} \times 55 \times \frac{21}{2}\right)=288.75 \mathrm{~cm}^{2}$