Question

What is the formula for the area of a circle?

Answer 1

`A=pi*r^2=` area of a circle

Answer 2

The formula `A = pi r^2` expresses the area of a circle in terms of its radius.

Explanation:

The number `pi` is defined as the ratio of the circumference of a circle to its diameter (i.e. to twice its radius), hence the formula `2 pi r`.

The area of a circle is given by the formula:

`A = pi r^2`

To see why, you can divide a circle into a number of equal segments and stack them head to tail to form a sort of parallelogram with 'bumpy' sides. The long sides will be about half the circumference in length - that is `pi r`, while the height of the parallelogram will be about `r`. So the area is seen to be about `pi r^2`.

This approximation gets better the more segments you have, but here's an animated illustration I put together with just `8` segments...