# Flakes

A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes".
Which is bigger: the content of the central square or the content of four chips?

Correct result:

S1 =  1
S2 =  1

#### Solution:

$a=1 \ \\ S_{1}=a^2=1^2=1$
$r_{1}=a/2=1/2=\dfrac{ 1 }{ 2 }=0.5 \ \\ r_{2}=\sqrt{ 2 }/2 \cdot \ a=\sqrt{ 2 }/2 \cdot \ 1 \doteq 0.7071 \ \\ \ \\ S_{3}=4 \pi \cdot \ r_{1}^2/2=4 \cdot \ 3.1416 \cdot \ 0.5^2/2 \doteq 1.5708 \ \\ S_{4}=\pi \cdot \ r_{2}^2=3.1416 \cdot \ 0.7071^2 \doteq 1.5708 \ \\ \ \\ S_{2}=S_{3}-S_{4}+S_{1}=1.5708-1.5708+1=1$

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