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

We know that area of the sector of the circle of radius $r=\frac{\theta}{360} \times \pi r^{2}$

Length of the arc $=\frac{\theta}{360} \times 2 \pi r$

But we have given that length of the arc 

So, $l=\frac{\theta}{360} \times 2 \pi r$...(1)

Area of the sector $=\frac{\theta}{360} \times \pi r^{2}$

Now we will adjust 2 in the following way,

Area of the sector $=\frac{\theta}{360} \times \frac{2 \pi r^{2}}{2}$

Area of the sector $=\frac{\theta}{360} \times 2 \pi r \times \frac{r}{2}$

From equation (1) we will substitute $\frac{\theta}{360} \times 2 \pi r=l$

Area of the sector $=l \times \frac{r}{2}$

Area of the sector $=\frac{1}{2} l r$

Therefore, area of the sector $=\frac{1}{2} l r .$