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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 $360\mathrm{\xb0}$.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 $\frac{120\mathrm{\xb0}}{360\mathrm{\xb0}}\mathrm{\pi}{r}^{2}$ square units (where the degree of sector is $120\mathrm{\xb0}$).

Area of quadrant circle:

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 $\frac{90\mathrm{\xb0}}{360\mathrm{\xb0}}\mathrm{\pi}{r}^{2}$ square units (where the degree of quadrant circle is $90\mathrm{\xb0}$).

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 $\frac{\mathrm{\theta}\mathrm{\xb0}}{360\mathrm{\xb0}}$ where $\left(\mathrm{\theta}=\frac{360\mathrm{\xb0}}{n}\right)$.

**Therefore the area of the sector of the circle**$A\phantom{\rule{0.147em}{0ex}}=\frac{\mathrm{\theta}\mathrm{\xb0}}{360\mathrm{\xb0}}\times \mathrm{\pi}{r}^{2}$

**square units.**

Important!

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.