Flakes

A circle was inscribed in the square. We draw a semicircle above each side of the square as above the diameter. This resulted in four chips.
Which is bigger: the area of the middle square or the area of the four chips?

Correct answer:

S₁ =  1
S₂ =  1

Step-by-step explanation:

$$\begin{gathered} a=1 \\ {S}_1=a^2=1^2=1 \end{gathered}$$

$$\begin{gathered} r_1=a/2=1/2=\frac{1}{2}=0.5 \\ {r}_2=\sqrt{2}/2\cdot a=\sqrt{2}/2\cdot 1\doteq 0.7071 \\ {S}_3=4\pi \cdot r_1^2/2=4\cdot 3.1416\cdot 0.5^2/2\doteq 1.5708 \\ {S}_4=\pi \cdot r_2^2=3.1416\cdot 0.7071^2\doteq 1.5708 \\ {S}_2=S_3-S_4+S_1=1.5708-1.5708+1=1 \end{gathered}$$

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