 ## Book: RS Aggarwal - Mathematics

### Chapter: 18. Area of Circle, Sector and Segment

#### Subject: Maths - Class 10th

##### Q. No. 23 of Exercise 18A

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23
##### The perimeter of a certain sector of a circle of radius 6.5 cm is 31 cm. Find the area of sector.

Given:

Radius of circle = 6.5 cm

Perimeter of sector = 31 cm

Now, Perimeter of sector = 2 × radius + Length of arc

Length of arc = × 2r × 2πr

Perimeter of sector = 2 × r + × 2r × π

= 2r × [1 + × π]

31 = 2 × 6.5 × [1 + × ]

31 = 13 × [1 + × ] = 1 + ×  - 1 = ×  = × θ = × 360 × …………………. (i)

Area of sector = × πr2

using (i), we have

Area = × 360 × × × × 6.5 × 6.5

= 18 × 3.25 = 58.5 cm2

Hence, the area of the sector is 58.5 cm2.

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