Area of Sector Question1

In this page area of sector question1 we are going to see solution of first question of the worksheet area of sector. After verifying the solution you can continue the quiz on the page itself.

Area of the sector = (θ/360) x Π r ² square units

(or)  Area of the sector = (1/2) x l r square units    

Question 1 :

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

Solution :

In this problem we need to find the area of the sector.For that we can use two formulas but from the given information we come to know that first we have to find the arc length

Perimeter of sector = 78 cm

                  L + 2r = 78 -------(1)

 Here L - arc length

       L = (θ/360) x 2 Π r

       L = (45/360) x 2 x (22/7) x r

       L = (45/180) x (22/7) x r

       L = (45/90) x (11/7) x r

       L = (1/2) x (11/7) x r

       L = (11r/14)

substitute L = 11r/14 in the first equation 

         (11r/14) + 2 r = 78

         (11r/14) + (2 r/1) = 78

         (11r/14) + (2 r x 14)/14 = 78

     (11 r + 28 r) /14 = 78

               (39 r/14) = 78 

                         r = 78 x (14/39)

                         r = 2 x 14

                         r = 28

from this we can find the value of and L and we can apply the second formula to get the answer or we can apply the first formula to get the answer.

Area of sector = (θ/360) x Π r²

                    = (45/360) x (22/7) x 28 x 28

                    = (45/180)  x 11 x 4 x 28

                    = (45/90) x 11 x 2 x 28

                    = (1/2) x 11 x 2 x 28                   

                    = 11 x 28                   

                    = 308 square cm


Question 2 :

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



(A) 242 square cm
(B) 315 square cm
(C) 231 square cm




Question 3 :

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



(A) 385 square cm
(B) 416 square cm
(C) 105 square cm




Question 4 :

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



(A) 120.5 square cm
(B) 115.5 square cm
(C) 123.5 square cm




Question 5 :

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



(A) 180 square cm
(B) 498 square cm
(C) 462 square cm




Question 6 :

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



(A) 180 square cm
(B) 150 square cm
(C) 162 square cm




Question 7 :

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



(A) 296 square cm
(B) 285 square cm
(C) 252 square cm




Question 8 :

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



(A) 125 square cm
(B) 185 square cm
(C) 152 square cm




Question 9 :

Find the area of sector whose perimeter is 147 cm and radius is 35 cm   area of sector question1



(A) 1347.5 square cm
(B) 1855.6 square cm
(C) 1521.3 square cm




Question 10 :

Find the area of sector whose length of arc is 21 cm and radius is 66 cm           area of sector question1



(A) 347 square cm
(B) 693 square cm
(C) 842 square cm




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Area of Sector Question1 to Area of Sector Worksheet