# Areas of Sector and Segment of a Circle

**Sector of a Circle**

Sector of a Circle is the portion of circular region enclosed by the radii and the corresponding arc.

âˆ´ shaded region OAPB is a sector of the circle with centre O.

**Segment of a Circle**

Segment of a Circle is the circular region enclosed between a chord and the corresponding arc.

OAPB is called the minor sector.

OAQB is called the major sector.

In the figure APB is the minor segment and AQB is the major segment.

Let OAPB be a sector of a circle O and radius r. Let the be Î¸

We know that Area of a circle = Ï€r^{2} sq units

The circle can be considered as a circular region, with a sector forming an angle of 360^{0}.

# Area of the sector of angle (Î¸)

By applying unitary method, we find that when degree measure of the angle at the centre is 360^{0}then the area of the sector = Ï€r

^{2}sq units

Â

When degree measure of angle at centre is 1, area of the sector = sq units

Therefore when degree measure of the angle at the centre is Î¸ , area of sector = Ã— Î¸ = Ã— Ï€r^{2} sq units

Length of the arc of a sector of angle Î¸

Let us consider the whole length of the circle as 2Ï€r (of angle 360Â°) units

âˆ´ By Unitary Method

The length of the arc of a sector of angle (Î¸) = units

**Area of the Segment**

Let us consider a circle with centre at O, of radius r units

Area of segment APB = Area of sector OAPB â€“ Area of Î” OAB

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = - Area of Î” OAB

**Note**

Area of major sector OAQB = Ï€ r^{2} â€“ area of minor sector OAPB

Area of major segment AQB = Ï€ r^{2} â€“ area of minor segment APB