AREA OF SECTORS WORKSHEET

Problem 1 :

Find the area of the sector whose radius and central angle are 42 cm and 60° respectively.

Problem 2 :

Find the area of the sector whose radius and central angle are 21 cm and 60° respectively.

Problem 3 :

Find the area of the sector whose radius and central angle are 4.9 cm and 30° respectively.

Problem 4 :

Find the area of the sector whose radius and length of arc are 6 cm and 20 cm respectively.

Problem 5 :

Find the area of the sector whose diameter and length of arc are 10 cm and 40 cm respectively.

Problem 6 :

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.

Problem 7 :

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

Problem 8 :

Find the area of the sector whose radius is 20 cm and perimeter is 110 cm.

Problem 1 :

Find the area of the sector whose radius and central angle are 42 cm and 60° respectively.

Solution :

Area of the sector  =  (θ/360°) x πr2

Substitute r = 42, θ = 60° and π  22/7.

(60°/360°)(22/7)(42)2

=  (1/6) x (22/7) x 42 x 42

=  924

So, the required area is about 924 cm2

Problem 2 :

Find the area of the sector whose radius and central angle are 21 cm and 60° respectively.

Solution:

Area of the sector  =  (θ/360°) x πr2

Substitute r = 21, θ = 60° and π  22/7.

(60°/360°)(22/7)(21)2

=  (1/6) x (22/7) x 21 x 21

=  231

So, the required ares is about 231 cm2.

Problem 3 :

Find the area of the sector whose radius and central angle are 4.9 cm and 30° respectively.

Solution :

Area of the sector  =  (θ/360°) x πr2

Substitute r = 4.9, θ = 30° and π  22/7.

(30°/360°)(22/7)(4.9)2

=  (1/12) x (22/7) x 4.9 x 4.9

6.3

So, the required area is about 6.3 cm2.

Question 4 :

Find the area of the sector whose radius and length of arc are 6 cm and 20 cm respectively.

Solution :

Area of the sector  =  (lr/2) square units

Substitute r = 6 and l = 20.

=  (20 x 6) / 2

=  60 cm2

Question 5 :

Find the area of the sector whose diameter and length of arc are 10 cm and 40 cm respectively.

Solution :

Diameter  =  10 cm

Radius  =  Diameter / 2  =  10/2  =  5 cm

Area of the sector is

=  (lr/2) square units

Substitute r = 5 and l = 40.

=  (40 x 5) / 2

=  100 cm2

Problem 6 :

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 :

Area of the sector  =  lr/2

Substitute r = 21 and l = 66.

=  (66 x 21) / 2

=  693 cm2

Using the area of the sector 693 cm2, find the central angle θ.

Area of the sector  =  693 cm2

(θ/360°) x πr2  =  693

Substitute r = 21 and π  22/7.

(θ/360) x (22/7) x (21)2  =  693

(θ/60°) x 231  =  693

θ  =  693 x (60°/231)

θ  =  180°

Problem 7 :

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

Solution :

Given : Radius is 35 cm and perimeter of the sector is 147 cm.

Perimeter of sector  =  147 cm

l + 2r  =  147

l + 2(35)  =  147

l + 70  =  147

l  =  77 cm

Area of the sector is

=  (lr/2) square units

Substitute r = 35 and l = 77.

=  (77 x 35) / 2

=  2695/2

=  1347.5 cm2

Problem 8 :

Find the area of the sector whose radius is 20 cm and perimeter is 110 cm.

Solution :

Given : Radius is 20 cm and perimeter of the sector is 110 cm.

Perimeter of sector = 110 cm

l + 2r  =  110

l + 2(20)  =  110

l + 40  =  110

l  =  70 cm

Area of the sector is

=  (lr/2) square units

Substitute r = 20 and l = 70.

=  (70 x 20) / 2

=  700 cm2

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