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You can split the circle up, into a lot of slices (as when you cut a Pizza). If the slices are very thin, their shape will be quite similar to thin triangles. When you add up all these triangles, you get an area of (1/2) x radius x perimeter.

I am not sure whether this was the original derivation of the area, but it's certainly one way it can be done.

You can also split the circle into small shapes in other ways (for example, vertical strips), and add up the pieces.

Such techniques are known as "integration", and you learn them in the subject called "calculus".

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Hilmar Zonneveld

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Q: How was the formula for area of cicle derived?
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