Answer :

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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