AREA OF SECTOR QUESTION3

Area of sector question3 :

Here we are going to see the solution of third question of the worksheet area of sector.

Question 3 :

Find the area of sector whose perimeter is 92 cm and central angle is 36°

Solution :

Based on the given information, let us draw a rough diagram

Perimeter of sector  =  92 cm   

L + 2r = 92 -------(1)

L = (θ/360) x 2 Π r

L = (36/360) x 2 x (22/7) x r

L = (1/10) x 2 x (22/7) x r

L = (1/5) x (22/7) x r

L = (22/35) x r

L = (22r/35)

By applying the value of L = 22r/35 in the (1)st equation, we get 

(22 r/35) + 2 r = 92

(22r/35) + (2 r/1) = 92

(22 r/35) + (2 r x 35)/35 = 92

(22 r + 70 r) /35 = 92

(92 r/35) = 92 

r = 92 x (35/92)

r = 35

So, L =  22(35)/35

L  =  22 cm

Area of sector  =  lr/2

  =  22(35)/2

=  11 (35)

  =  385 cm²

Hence, area of the required sector is 385 cm².

Area of sector worksheet - Practice questions

(1)  Find the area of sector whose perimeter is 78 cm and central angle is 45°

(2)  Find the area of sector whose perimeter is 64 cm and central angle is 60°

(3)  Find the area of sector whose perimeter is 92 cm and central angle is 36°

(4)  Find the area of sector whose perimeter is 43 cm and radius is 10.5 cm

(5)  Find the area of sector whose perimeter is 86 cm and radius is 21 cm

(6)  Find the area of sector whose perimeter is 56 cm and radius is 10 cm

(7)  Find the area of sector whose perimeter is 64 cm and radius is 14 cm

(8)  Find the area of sector whose perimeter is 45 cm and radius is 10 cm

(9)  Find the area of sector whose perimeter is 147 cm and radius is 35 cm   

(10)  Find the area of sector whose length of arc is 21 cm and radius is 66 cm

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