Area of sector formula and examples

Formula

 Area of Sector Formula & Examples

 Area of sector formula & examples, Sector is a portion of a circle which is enclosed between its two radius and the arc adjoining them. To know more here is a example, A “pie-slice” part of a circle – the area between two radiuses and the connecting arc of a circle.

What is the Area of a Sector?

MEANING : The area of a sector is the region enclosed by the two radius of a circle and the arc. In simple words, the area of a sector is a fraction of the area of the circle. To know more In brief the area of sector, it is the central angle of 360, times the area of the circle, to get more let’s example,

  • if the central angle is 60, and the two radiuses forming it are 20 inches, you would divide 60 by 360 to get 1/6.

How to Find the Area of a Sector?

If you want to calculate area of a sector, you need to know the following two parameters:

  • you should have to know length of circle’s radius.
  • you should have measure of the central angle or the length of the arc. The central angle is the angle subtended by an arc of a sector at the center of a circle. The central angle can be given in degrees or radians.

With the upper two parameters, finding the area of a circle is as easy as ABCD.  It is just a matter of plugging in the values in the area of the sector formula given below.

Formula for area of a sector

There are three formulas for calculating the area of a sector. Each of these formula is applied depending on the type of information given about the sector.

Area of a sector when the central angle is given in degrees.

If it is given that angle of the sector  in degrees, then the formula for the area of a sector is given by,

FORMULA : Area of a sector = (θ/360) πr2

A = (θ/360) πr2

Where, θ = the central angle in degrees

Pi (π) = 3.14 and r = the radius of a sector.

Area of a sector given the central angle in radians.

If you are having central angle  in radians, then the formula for calculating the area of a sector is;

FORMULA : Area of a sector = (θr2)/2

Where, θ = the measure of the central angle given in radians.

Area of a sector given the arc length

If, the length of the arc and the area of a sector is given by,

FORMULA : Area of a sector = rL/2

L = arc length.

Let’s work out a couple of example problems involving the area of a sector.

Example 1

Calculate the area of the sector shown below.

Area of sector

Solution

Area of a sector = (θ/360) πr2

= (130/360) x 3.14 x 28 x 28

= 888.97 cm2

Example 2

Calculate the area of a sector with a radius of 10 yards and an angle of 90 degrees.

Area of a sector = (θ/360) πr2

A = (90/360) x 3.14 x 10 x 10

= 78.5 sq. yards.

Example 3

Find the radius of a semi – circle with the area of 24 inches squared.

Solution

A semi-circle is the same as half a circle, therefore, the angle θ = 180 degrees.

A= (θ/360) πr2

24 = (180/360) x 3.14 x r2

24 = 1.57r2

Divide both sides by 1.57.

15.287 = r2

Find the square root of both sides.

r = 3.91

So, the radius of the semi-circle is 3.91 inches.

EXAMPLE 4

Find the central angle of a sector whose radius is 56 cm and area, is 144 cm2.

Solution

A= (θ/360) πr2

144 = (θ/360) x 3.14 x 56 x 56.

144 = 27.353 θ

Divide both sides by θ.

θ = 5.26

Thus, the central angle is 5.26 degrees.

Example 5

Find the area of a sector with the radius of 8 m and central angle of 0.52 radians.

Solution

Here, the central angle is in radians, so we have,

Area of a sector = (θr2)/2

= (0.52 x 82)/2

= 16.64 m2

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