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I understand the logic behind the area of a circle been equal to $r^2\pi$, but I can't figure out why the perimeter of a circle couldn't be split into four approximately equal parts and then squared to give the same area. I suppose it have something to do with pi having a infinite decimal representation.

Many Thanks,

Jhonny

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closed as unclear what you're asking by Yves Daoust, Henrik, I am Back, Antonios-Alexandros Robotis, Namaste Oct 5 '17 at 15:49

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Hint: Same perimeter of two figures doesn't mean the area enclosed by them is equal.

So you cannot cut a circle into four pieces of length $\pi r/2$ and get an area of $\pi^2 r^2/4$

If we follow you reasoning, we can cut the circle into four pieces with two of them having $\text{length}\rightarrow\pi r$ and other two having $\text{length}\rightarrow 0$ and arrange them to form a rectangle having $\text{area}\rightarrow 0$

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  • $\begingroup$ Spot on. Many Thanks $\endgroup$ – JhonnyWhiteWalker Oct 5 '17 at 10:46

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