Why does the formula for finding the area of a circle work? a = π r²

See below.

Step-by-step explanation:

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.

Hope this helps.

this is false ^.^ lol