Formula for calculating the area of ​​a circular sector

Circular sector is a very special geometric form in plane geometry. The following article introduces to you the concept of what a sector is, the formula for calculating the area of ​​a circular sector, and the circumference of a circular sector. Please refer to it.

Round fan shape

• What is a fan shape?
• Formula for calculating the area of ​​a fan
• Formula for calculating the circumference of a circular sector
• Example of calculating the area of ​​a circular sector, the circumference of a circular sector

What is a fan shape?

The shape bounded by two radii OA, OB and circular arc AB as shown below is called a circular sector.

So a sector is a part of a circle bounded by two radii and an arc.

Formula for calculating the area of ​​a fan

Let S be the area of ​​a circular sector, then the formula for calculating the area of ​​a circular sector has 2 expressions:

or

In there:

• Sis the area of ​​a circular sector
• Ris the radius of the circle, as in the picture then R = OA = OB
• ℓis the arc length, according to the figure, ℓ has the same length as arc AB.

Formula for calculating the circumference of a circular sector

The formula for calculating the perimeter of a circular sector is determined by the formula:

In there:

• Cis the circumference of the fan
• Ris the radius of the circle with center O
• ℓis the arc length

Example of calculating the area of ​​a circular sector, the circumference of a circular sector

Lesson 1 :

Calculate the area of ​​a circular sector when radius R = 5 cm, angle n = 30º.

Solution : Applying the formula for calculating the area of ​​a fan, we have:

Lesson 2 :

Calculate the area of ​​a circular sector when knowing the radius R = 7 cm, arc length ℓ = 5 cm.

Solution : Applying the formula for calculating the area of ​​a fan, we have:

Lesson 3:

Calculate the perimeter of a sector with area 8 cm2 and arc length 5 cm.

Solution : We have:

Based on the formula for calculating the perimeter of a fan, we have: C = 2R + ℓ = 2.3.2 + 5 = 11.4 (cm).

Also don't miss the series of articles on calculating the area of ​​a circle , the area of ​​a pyramid and a series of other shapes.