A sector is a part of the circle

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Perimeter of sector will be the distance around it

Perimeter of Sector - Part 2

 

Thus,

  Perimeter of sector = πœƒr + 2r

   = r(πœƒ + 2)

Where πœƒ is in radians

 

If angle is in degrees,

πœƒ = Angle × π/(180°)

 

Let us take some examples:

 

Find perimeter of sector whose radius is 2 cm and angle is of 90° 

Perimeter of Sector - Part 3

First,

We need to convert angle in radians

πœƒ = Angle in degree × π/(180°)

πœƒ = 90° × π/(180° )

πœƒ = π/4

 

And Radius = r

            = 2 cm

 

Now,

  Perimeter of sector  = r (πœƒ + 2)

    = 2 (π/4+2)

    = 2 ((π + 2 × 4)/4)

    = 2 ((π + 8)/4)

    = (π + 8)/4 cm

 

Find perimeter of sector whose radius is 2 cm and angle is π/4 radians

Perimeter of Sector - Part 4

Radius = r

     = 2 cm

 

Angle (in radians) = πœƒ

      = π/4

Now,

  Perimeter of sector = r (πœƒ + 2)

  = 2 (π/4+2)

  = 2 ((π + 2 × 4)/4)= 2 ((π + 8)/4) = (π + 8)/4 cm

 

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.