Question

find the area of a sector of a circle whose radius is R and length of arc is l

Answer 1

Let the angle subtended by arc at the centre be $\theta$

Here length of the arc is l

We know that length of the arc = $\frac{\theta}{360}\times 2\pi R$

∴ $\frac{\theta}{360}\times 2\pi R$ = l

$\frac{\theta}{360} = \frac{l}{2\pi R}$ ------ ( i )

Now

Area of sector = $\frac{\theta}{360} \pi R^2$

= $\frac{l}{2 \pi R} \times \pi R^2$    [from ( i ) ]

Which gives us Area of Sector = $\frac{lR}{2}$