In mathematics, we learn how to find the area of a circle. In this blog, we will discuss what is a sector, segment, chord & how to find the area of a sector & segment of a circle.

# Sector, Segment & Chord of a Circle?

*Radius:-*

*It is a fixed-length from the centre to the boundary of a circle. It is always constant for a circle. As shown below OA & OB.*

*Diameter:-*

*It is twice of a radius. It always passes through the centre of the circle.*

**Diameter = 2×Radius.**

*Chord:-*

*It is a straight line in a circle which touches the boundary of the circle from both sides. As shown below PQ.*

*The diameter is the longest chord of any circle.*

*Sector:-*

*It is a region of a circle which is enclosed between two radii & an arc of a circle. As shown above. It may be classified as-*

**Minor sector**- It covers less area between two radii & an arc of a circle.**Major sector**- It covers more area between two radii & an arc of a circle.

*Segment:-*

*It is a region between an arc & a chord of a circle. As shown above. It may be classified as-*

**Minor segment**- It covers less area between a chord & an arc of a circle.**Major segment**- It covers more area between a chord & an arc of a circle.

## How to find the area of Sector?

For finding the area of a sector of a circle we have a formula-

**Area of sector = (Î¸/360Âº)×Ï€r²**

Where

- Î¸=Angle of minor sector or major sector.
- Ï€=22/7 or 3.14
- r=radius of circle

For better understanding, we take an example. Let's discuss-

### Question:-

**Find the area of the sector with radius 5 cm & if the angle of the sector is 80Âº.**

### Answer:-

*First, we draw an image for better understanding.*

*In the above picture, we take a circle in which a minor sector (AOB) is shown.*

*Because it has less area or less angle so we are considering it as the minor sector.*

*Given-**The angle of the sector(AOB)=80Âº*

*Radius of circle=5cm*

*Put all the values in the formula-*

*Area of sector = (Î¸/360Âº)×Ï€r²*

*(Î¸/360Âº)Ï€r²**(80Âº/360Âº)(22/7)×(5)²**(1/4.5)(22/7)×25**(22/31.5)×25**(22×25)/31.5**17.46 cm²*

*We get the area of minor sector 17.46 cm².*## How to find the area of Segment?

Here the same, for finding the area of the segment we have a formula-

**Area of segment = r²{Ï€Î¸/360Âº-(sin(Î¸/2)cos(Î¸/2)}**

This formula works when we know the values of sin & cos.

Where

- Î¸= Angle of the segment
- r= Radius of circle
- Ï€=22/7 or 3.14

For better understanding, we take an example. Let's discuss-

### Question

**Find the area of the segment with radius 5 cm & if the angle of the segment is 90Âº.**

### Answer

*First, we draw an image for better understanding.*

*In the above picture, we take a circle in which a minor segment is shown.*

*Because it has less area or less angle so we are considering it as the minor segment.*

*Given-**The angle of the segment=90Âº*

*Radius of circle=5cm*

*Put all the values in the formula-*

*Area of segment = r²{Ï€Î¸/360Âº-(sin(Î¸/2)cos(Î¸/2)}*

*r²{Ï€Î¸/360Âº-(sin(Î¸/2)cos(Î¸/2)}**5²{(22/7)(90Âº/360Âº)-sin(90/2)×cos(90/2)}**25{(22/7)(1/4)-sin45Âº×cos45Âº**25{(22/7)(1/4)-(1/√2)×**(1/√2)}**25{(22/28)-(1/2)}**25{(11/14)-(1/2)}**25×0.285**7.125cm²*

*We get the area of minor segment 7.125cm².***In this way, we may find the area of sector & segment of a circle.**

**THANK YOU...**