1. Length of arc, Area of sector and Perimeter of sector

2. Area of the sector r A B o
Sector
OAB
Consider a circle of radius r. The area of the circle is πr2. The orange part is called a sector. The name of the sector is The area of a sector is a part of the area of the circle.
OAB
Animation to be checked

3. of the circle(3600) multiplied by the area of the circle.
The area of an arc is equal to ratio of central angle(Ɵ) of the sector to central angle
of the circle(3600) multiplied by the area of the circle.
Central angle of sector
Central angle of circle
Area of the arc =
x area of circle Ɵ
∴ Area of the arc =
For a full circle, the central angle of the sector is equal to central angle of circle
which is 360o. So, the area of the full circle is
which is the area of the circle.

4. Example 1: Find the area of a sector of a circle with radius 42 cm and central angle of
Solution:
Given: Radius (r) = 42 cm , Central angle of sector (Ɵ)= 60o
To Find: Area of sector
Area of sector =
Area of sector =
Area of sector
Area of sector = 22 x 42 = 924 cm2
Ans: Area of sector = 924 cm2 O A B
42 cm
60o 1
(Dividing 60 and 360 by 60) 6 6
(substituting π = and r = 42)

5. Example 2: Find the i) length of the arc and ii) area of the sector of a circle with
radius 84 cm and central angle of sector 72o.
Solution:
Given: Radius (r) = 84 cm , Central angle of sector (Ɵ)= 72o
To Find: i) Length of arc ii) Area of sector
i) Length of the arc =
Length of the arc =
84 cm O A B
72o 1
(Dividing 72 and 360 by 72) 5 12
(substituting π = and r = 84)
= cm

6. ii) Area of sector = Area of sector = Area of sector = = 4435
ii) Area of sector = Area of sector = Area of sector = = cm2 Ans: Length of the quadrant = cm Area of sector = cm2 1
(Dividing 72 and 360 by 72) 5 12

7. Perimeter of a sector
What is perimeter? If we walk along the border of any shape, we get its perimeter. Perimeter of a sector Consider a sector of radius r and with the length of the arc l The perimeter of a sector is the sum of length of the arc and length of two radii. Perimeter of a sector = length of arc + length of 2 radii Perimeter of a sector = l + 2r
( where l = )

8. Example 3: Find the perimeter of a sector with radius 14 cm and central angle 45o Solution: Given: Radius (r) = 14 cm , Central angle of sector (Ɵ) = 45o To find: Perimeter of sector We know that, perimeter of a sector is the sum of length of the arc and length of two radii Perimeter of a sector = l + 2r Length of the arc (l) =
( where l = )
(Dividing 45 and 360 by 45) 8 4 11 2
(substituting π = and r = 14) 2
= 11 cm

9. Perimeter of a sector = l + 2r = l + 2 x r (substituting l= 11 and r = 14 , we get) = 11 + (2 x 14) = = 39 cm Ans: Perimeter of the sector = 39 cm

10. Try These
The radius of a sector is 21cm and its central angle is 120 ° . Find
area of the sector and
perimeter of sector