### Theory:

Area of circle:
The area of a circle is defined as the number of square units inside that circle. It is pi times the radius square. The degree of the circle is $360\mathrm{°}$.

Area of circle ($$A$$) $$=\pi r^2$$ square units, where $\mathrm{\pi }=3.14$.
Area of a semicircle:
The area of a semicircle is defined as the number of square units inside that circle. It is half($$1/2$$) pi times the radius square. The degree of the semicircle is $$180°$$.

Area of a semicircle $$A=\frac{1}{2}\pi r^2$$ square units.

It can also be written as $$\frac{180^\circ}{360^\circ}\pi r^2$$ square units (where the degree of semicircle is $$180^\circ$$).
Area of one-third circle:
The area of one-third circle is defined as the number of square units inside that circle. It is one by three ($$1/3$$) pi times the radius square. The degree of the one-third circle is $$120°$$.

Are of a one - third of circle $$A=\frac{1}{3}\pi r^2$$ square units.

It can also be written as $\frac{120\mathrm{°}}{360\mathrm{°}}\mathrm{\pi }{r}^{2}$ square units (where the degree of sector is $120\mathrm{°}$).
The area of quadrant circle is defined as the number of square units inside that circle. It is one by quarter($$1/4$$) pi times the radius square. The degree of the quadrant circle is $$90°$$.
Area of a quadrant circle $$A=\frac{1}{4}\pi r^2$$ square units.
It can also be written as $\frac{90\mathrm{°}}{360\mathrm{°}}\mathrm{\pi }{r}^{2}$ square units (where the degree of quadrant circle is $90\mathrm{°}$).
From the above explanation, we get the idea that the area of a sector is equal to the number of square units inside that circle. It is pi time the radius square by $\frac{\mathrm{\theta }\mathrm{°}}{360\mathrm{°}}$ where $\left(\mathrm{\theta }=\frac{360\mathrm{°}}{n}\right)$.
Therefore the area of the sector of the circle $A\phantom{\rule{0.147em}{0ex}}=\frac{\mathrm{\theta }\mathrm{°}}{360\mathrm{°}}×\mathrm{\pi }{r}^{2}$ square units.
If a circle of radius($$r$$) units divided into $$n$$ equal sectors, then the
area of the sector = $$\frac{1}{n}\times \pi r^2$$ square units.