In this applet, we consider a circle, and divide the circle into slices of sectors. Then, we visualize the circle's area by rearranging the slices to form a rectangle. [br][br]We know that[br]1. the formula of Area(Rectangle) = Length x Breath[br]2. the formula of Circumference (Circle)=2⋅π⋅r. [br]3. In this rearrangement, [br] (i) area of circle =area of rectangle[br] (ii) the approximate length of the rectangle is half of the circumference.[br][br]Now, [br]Combining these three facts/formula, [br] Area of circle = area of rectangle [br] = ( π⋅r)⋅(r) [br] = π⋅r^2. [br]Conclusion, although we use approximations for the length and breath, the resulting formula for the circle's area is exact, because we can continue the approximation with large number of slices.[br]