A sector is a part of the circle

Perimeter of sector will be the distance around it

Thus,

Perimeter of sector = 𝜃r + 2r

= r(𝜃 + 2)

Where 𝜃 is in radians

If angle is in degrees,

𝜃 = Angle × π/(180°)

Let us take some examples:

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

First,

We need to convert angle in radians

𝜃 = Angle in degree × π/(180°)

𝜃 = 90° × π/(180° )

𝜃 = π/4

And Radius = r

= 2 cm

Now,

Perimeter of sector = r (𝜃 + 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

Radius = r

= 2 cm

Angle (in radians) = 𝜃

= π/4

Now,

Perimeter of sector = r (𝜃 + 2)

= 2 (π/4+2)

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

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