In the given figure, the length of arc AB is equal to twice the length of radius r of the circle. Find the area of sector OAB in terms of the radius r.

r²

We know that,

l = r × θ 

Area of an arc =  \(\frac{ θ }{360 }\) × πr²  

According  to the question,

Length of the arc AB = 2r 

Here, we have length of the arc = 2r 

= l = r × θ 

= 2r = r × θ

= θ = 2 

Area of the sector = \(\frac{ θ }{360 }\) × πr² 

= \(\frac{ 2 }{360 }\) × 180 × r²  =  r²