The formula for finding the area of the circle works because they made it especially for it. I don’t really know how else to describe it, it simply just works.
If we divide the circle into a large number of sectors and line them up in a straight line it will be close to a rectangle .
The area of the rectangle will be approximately the area of the circle.
If we have an infinite number of these sectors we get a rectangle whose width is the radius r of the circle. We know that the circumference of a circle is equal to 2πr, so our rectangle will be πr long and r wide. Area = πr*r = πr^2.
Draw a circle and try deriving the rectangle as above and it should be clearer.
