A circle's area is found using the formula:But where does this formula come from?Let's find out ... |

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 ... the rectangle.
Maybe you're wondering how on earth you can rearrange pieces of a circle to make a rectangle! Well, just watch ... it's easy!We'll start with the circle that we want to break up: Let's break the circle into eighths instead:
these pieces into a rectangular shape:
look like a rectangle ... but we're not there yet! The next step is to go back and try splitting the circle into sixteenths. Here are the pieces:
A = L x W... but this shape does not have straight sides, so the formula wouldn't be very accurate.Let's go one step further, and break up the circle into a whole bunch of little pieces. When we rearrange all the pieces, the shape would look something like this:still not perfectly straight ... they are definitely a little bumpy.Can you visualize what would happen if we kept going? If we continued to break the circle up into tinier and tinier pieces? Eventually, the bumps would become so small that we couldn't see them, and the top and bottom of the shape would appear perfectly straight. This is what we would see: 'How long are the length and width of our rectangle made from circle parts?'Let's go back to an earlier picture, so you can see the circle parts more clearly: top of the 'rectangle', and the other half of the circle, also length , goes on the bottomr.r |