**Circular sector** . There are different geometric figures such as the square , the rectangle , the trapezoid , the circle , the circumference , etc. Each one has its definitions and elements and the area , perimeter and length can be calculated .

Long ago, men struggled to make these calculations because of the importance of different objects, mainly circular, used in practice. From there began the study of the different elements that compose them, including the circular sector.

## Summary

[ hide ]

- 1 Applications
- 2 Area of a circular sector
- 1 Example

- 3 Perimeter of a circular sector
- 1 Arc length
- 2 Example

- 4 Source

## Applications

Knowing about the circular sector, the area covered by a swing when rocking can be calculated.

You can also calculate the area covered by the pendulum of the wall clock . The amount of square meters that an orchard covers with this geometric shape and with it the amount of materials that will be used to enclose its limits.

## Area of a circular sector

A ratio can be obtained to calculate the area of a circular sector as shown below.

### Example

Find the area of a circular sector that is 20 ° wide in a circle 2m radius.

## Perimeter of a circular sector

The perimeter is the sum of the length of its sides, in this case it has two equal sides which is the radius of the circle and an arc, therefore it is necessary to find the length of the arc first.

### Bow length

To calculate the length of an arc of circumference , a proportion must be established where ** L** is the length of the circumference,

**is the length of the arc,**

*b***is the width of the corresponding central angle and 360º is the total width of the circle. Being said proportion as shown below:**

*a*### Example

From a circumference of 4 cm radius, calculate the length of an arc that is 30º wide.

If the arc length corresponding to the circular sector and the radius of the circumference to which it belongs are already known, its perimeter can be calculated as follows: