Area – Circles and Pi

The Area of a Circle

But how do we actually calculate the area of a circle? Let’s try the same technique we used for finding the area of quadrilaterals: we cut the shape into multiple different parts, and then rearrange them into a different shape we already know the area of (e.g. a rectangle or a triangle).

The only difference is that, because circles are curved, we have to use some approximations:

Here you can see a circle divided into ${toWord(n1)} wedges. Move the slider, to line up the wedges in one row.

If we increase the number of wedges to ${n1}, this shape starts to look more and more like a .

The height of the rectangle is equal to the of the circle. The width of the rectangle is equal to of the circle. (Notice how half of the wedges face down and half of them face up.)

Therefore the total area of the rectangle is approximately A=πr2.

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The Area of a Circle