In this page area of sector question3 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**°

**Question 2 :**

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

**Question 3 :**

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

**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 = 92 cm

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

Here L - arc length

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)

substitute L = 22 r/35 in the first equation

(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

r = 35 cm

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

= (36/360) x (22/7) x 35 x 35

= (1/10) x (22/7) x 35 x 35

= (1/2) x (22/7) x 7 x 35

= 1 x 11 x 35

= 385 square cm

**Question 4 :**

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

**Question 5 :**

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

**Question 6 :**

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

**Question 7 :**

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

**Question 8 :**

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

**Question 9 :**

**Find the **** area of sector whose perimeter is 147 cm and radius is 35 cm **area of sector question3

**Question 10 :**

**Find the **** area of sector whose length of arc is 21 cm and radius is 66 cm **area of sector question3

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