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Published byBarnard Harrison Modified over 9 years ago

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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!

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Does this resemble any shape you are familiar with?

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

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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

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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.

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