Question

Write the area of the sector of a circle whose radius is r and length of the arc is l. 

Answer 1

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`