How does the area of a circle relate to the area of a parallelogram?

1 Answer
Sep 15, 2015

If you divide a circle into a number of equal segments then stack them in a row head-to-tail, the resulting shape is like a parallelogram with bumpy sides, with the same area as the circle.


As you make the segments smaller and smaller, the parallelogram becomes more of a rectangle with shorter side equal to the radius of the circle #r# and longer side #pi r# - half of the circumference of the circle.

Hence we get the formula #pi r^2# for the area of a circle of radius #r#.

enter image source here