Question

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

Answer 1

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.

Explanation:

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`.