Why the area of a circle is not equal to $\frac{(r^2\pi^2)}{4}$? [closed]

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

closed as unclear what you're asking by Yves Daoust, Henrik, Vidyanshu Mishra, Antonios-Alexandros Robotis, NamasteOct 5 '17 at 15:49

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• Pi being infinite? – астон вілла олоф мэллбэрг Oct 5 '17 at 10:32
• – Dr. Sonnhard Graubner Oct 5 '17 at 10:32
• Your formula is correct, provided you adjust with the factor $\approx 1.273239544735$ to take curvature into account. – Yves Daoust Oct 5 '17 at 10:39
• Why don't you divide the perimeter into three equal parts and use the formula for the area of an equilateral triangle? – Professor Vector Oct 5 '17 at 10:45
• @Professor Vector I think, there is a word "disc". – Michael Rozenberg Oct 5 '17 at 11:22

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 $\text{area}\rightarrow 0$