Question 313294
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The area of a circle with radius *[tex \Large r] is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A_c\ =\ \pi r^2]


The perimeter of a square with side measure *[tex \Large s] is:



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P_s\ =\ 4s]


But for this square and circle:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ s\ =\ r]


And


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A_c\ =\ P_s]


Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \pi s^2\ =\ 4s]


Divide both sides by *[tex \Large \pi s]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ s\ =\ \frac{4}{\pi}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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