What we're going to do is break up a circle into little pieces, and then reassemble it into a shape that we know the area formula for ...

Maybe you're wondering how on earth you can rearrange pieces of a circle.

Well, just watch ... it's easy!

Does this resemble any shape you are familiar with?

Does this resemble any shape you are familiar with?

Does this resemble any shape you are familiar with?

How are the length and width of a rectangle made out of circle parts?

The original circle's outside length was the distance around, or the circumference of the circle:

Half of this distance around r goes on the top of the 'rectangle', and the other half of the circle, also length r, goes on the bottom

In other words, all of the red and blue pieces add up to 2 r, the circumference. The sides are just the radius of each of the pieces, or the radius of the circle, r.So we know the length is *r, and the width is r.