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Question
Write the area of the sector of a circle whose radius is r and length of the arc is l.
Solution
We know that area of the sector of the circle of radius `r= θ/360xxpir^2`
But we have given that length of the arc =l
So, `l=θ/360xx2pir`.............(1)
`"Area of the sector"=θ/360xxpir`
Now we will adjust 2 in the following way,
`"Area of the sector"=θ/360xx(2pir^2)/2`
`"Area of the sector"=θ/360xx2pirxxr/2`
From equation (1) we will substitute` θ/360xx2pir=l`
Area of the sector =`lxxr/2`
Area of the sector=`1/2lr`
Therefore, area of the sector=`1/2 lr`
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