A sector is a part of the circle
Perimeter of sector will be the distance around it
Thus,
Perimeter of sector = πr + 2r
= r(π + 2)
Where π is in radians
If angle is in degrees,
π = 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
π = Angle in degree × π/(180°)
π = 90° × π/(180° )
π = π/4
And Radius = r
= 2 cm
Now,
Perimeter of sector = r (π + 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) = π
= π/4
Now,
Perimeter of sector = r (π + 2)
= 2 (π/4+2)
= 2 ((π + 2 × 4)/4)= 2 ((π + 8)/4) = (π + 8)/4 cm