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Question
The perimeter of a sector of circle of radius 5.7m is 27.2 m. Find the area of sector.
Solution
Radius = OA = OB (From fig) = r
= 5.7 m
Perimeter = 27.2 m
Let angle subtended at centre = ๐
Perimeter =`(theta/360^@× 2pir) `+ ๐๐ด + ๐๐ต
=`theta/360^@`× 2(5.7) × ๐ + 2(5.7)
=`(2pi(5.7)theta)/360^@`+ 11.4
`=( pi(5.7)theta)/180^@`+ 11.4 = 27.2
=`(pi(5.7)theta)/180^@`= 15.8
๐ด๐๐๐ ๐๐ ๐ ๐๐๐ก๐๐ =`theta/360^@× pir^2`
`=158.8/360×22/7`× 5.7 × 5.7
= 45.048 cm2
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