Area of a Sector

In this page area of a sector we are going to see how to find the area of any sector. Generally,we are having two formulas to find the area of any sector. We can use any other formula depending on the details given in the question.

Area of the sector = (θ/360) x Π r ² square units

(or)  Area of the sector = (1/2) x l r square units               


θ - central angle formed by the sector

L - length of arc

r - radius of the sector

We can use the first formula if the central angle(θ) formed by the sector and radius given. If the length of arc(L) is given we have to use the second formula only.

Example 1:

Find the area of the sector whose radius is 35 cm and perimeter is 147 cm.

Solution:

radius = 35 cm

Perimeter of sector = 147 cm

L + 2r  =  147 cm

Here r = 35 cm

L + 2 (35) = 147

L + 70 = 147

      L = 147 - 70

      L = 77 cm

Now we have the length of an arc and radius. So we have to use the second formula to find the area of the given sector.

Area of the sector = (1/2) x l r square units      

                                          = (1/2) x 77 x 35

                                          =  38.5 x 35

                                          = 1347.5 square units


Example 2:

Find the area of the sector and also find the central angle formed by the sector whose radius is 21 cm and length of arc is 66 cm.

Solution:

First,let us find the area of sector using length of an arc and radius.

Area of the sector = (1/2) x l r square units    

L = 66 cm

r = 21 cm

                                = (1/2) x 66 x 21

                                =  33 x 21 

                                = 693 square units

Area of the sector = 693 square units

(θ/360) x Π r ² = 693

(θ/360) x (22/7) x (21)² = 693

 θ = (693 x 7 x 360)/(22 x 21 x 21)

 θ = (693 x 360)/(22 x 3 x 21)

 θ = (231 x 180)/(11 x 21)

 θ = (21 x 180)/21

 θ = 180    area of a sector


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Area of a Sector to Formulas for Shapes