Formula for the area of a sector & Examples

In plane geometry, a sector is a common shape encountered in exercises. Moreover, sectors are frequently encountered in real-life scenarios, and you may need to calculate their areas. Join Mytour to explore the formula for the area of a sector & Examples in the article below.

1. What is a sector?

In plane geometry, a circular sector is a part of a circle, bounded by two radii and an arc between them.

2. Formula for calculating the area of a sector

The area of a circular sector is the area of a portion of a circle formed by two radii and the arc between them. To calculate the area of a circular sector, you need to use the angle between the two radii forming the circular sector and the area of the entire circle in which the circular sector lies.

The area of a sector is expressed as follows: The area of a sector is calculated as half of the area of a circle with radius R multiplied by an angle specified in radians.

The area of a sector with an angle of n degrees is calculated by the following formula:

S=πR2n∘360∘=lR2$S=\frac{\pi R^2{n}^{\circ }}{{360}^{\circ }}=\frac{lR}{2}$

Where:

• S is the area of the sector
• π is the constant Pi, approximately 3.14159
• R is the radius of the base circle of the sector
• n∘$n^{\circ }$ is the defined angle of the sector, measured in degrees
• l$l$ is the length of the arc n∘$n^{\circ }$

3. Illustrative Example

Example 1: Given a sector with a base circle radius R = 5cm and arc length 10 cm. Calculate the area of this sector.

Solution:

Applying the formula for calculating the area of a sector

S=πR2n∘360∘=lR2$S=\frac{\pi R^2{n}^{\circ }}{{360}^{\circ }}=\frac{lR}{2}$

We have:

S=lR2=10×52=502=25 cm2$S=\frac{lR}{2}=\frac{10\times 5}{2}=\frac{50}{2}=25{cm}^2$

So the area of the sector is 25 cm2$25{cm}^2$

Example 2: Calculate the area of a sector given the radius of the circle is 6 cm, and the angle n=30∘$n={30}^{\circ }$

Solution:

Using the formula for the area of a sector, we get:

S=πR2n∘360∘=π×62×30360=9,42 cm2$S=\frac{\pi R^2{n}^{\circ }}{{360}^{\circ }}=\frac{\pi \times 6^2\times 30}{360}=9,42{cm}^2$

Therefore, the area of the given sector is 9,42 cm2$9,42{cm}^2$

Above, Mytour has just shared with you the formula for calculating the area of a sector and specific examples illustrating how to calculate the area of a circular sector. We hope this article will help you gain more knowledge about sectors, understand the formula for calculating the area of a sector to apply when needed. Thank you for your interest and following this article.