In this page perimeter of sector question6 we are going to see solution of first problem in this worksheet. After verifying the solution you can continue the quiz on the page itself. After that you can try the remaining questions and check the answer by clicking option and submit answer.

**Perimeter of the sector = L + 2r**

L - length of sector

r - radius

**Question 1 :**

**Find the perimeter of sector whose radius is 42 cm and central angle is 60**°

**Question 2 :**

**Find the **** perimeter of sector whose radius is 21 cm and central angle is 120**°

**Question 3 :**

**Find the perimeter of sector whose radius is 35 cm and central angle is 72**°

**Question 4 :**

**Find the **** perimeter of sector whose radius is 10.5 cm and central angle is 36**°

**Question 5 :**

**Find the **** perimeter of sector whose area is 770 square cm and central angle is 90**°

**Question 6 :**

**Find the **** perimeter of sector whose area is 30.8 square cm and central angle is 72**°

**Solution :**

In
this problem we need to find the perimeter of the sector.For that we
can use the formula (L+2r). But here we don't have L,to find that first let us use the formula area of circle.

Area of circle = (θ/360) x Π r²

(θ/360) x Π r² = 30.8

Here θ = 72°

(72/360) x (22/7) x r² = 30.8

1/5 x (22/7) x r² = 30.8

r² = 30.8 x 7/22 x (5/1)

r² = 2.8 x (7/2) x 5

r =
√1.4 x 7 x 5

r = √49

r = 7 cm

length of arc = (θ/360) x 2 Π r

= (73/360) x 2 x (22/7) x 7

= (1/5) x 2 x 22

L = 8.8

**Perimeter of the sector = L + 2r**

** **= 8.8 + 2 (7)

** **= 8.8 + 14

** **= 22.8 cm

**Therefore perimeter of sector = 22.8 ****cm**

**Question 7 :**

**Find the **** perimeter of sector whose area is 616 square cm and central angle is 90**°

**Question 8 :**

**Find the ****perimeter of sector** whose area is 154 square cm and radius is 28

**Question 9 :**

**Find the ****perimeter of sector** whose area is 77 square cm and radius is 14

**Question 10 :**

**Find the ****perimeter of sector** whose length of arc is 56 cm and radius is 21

These are the questions in the topic perimeter of sector question6.

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