Eq triangle minus arcs

In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts.

Correct result:

S =  0.1613 cm²

Solution:

$$\begin{gathered} a=2\text{ cm } \\ r=1\text{ cm } \\ {S}_1=\pi \cdot r^2\mathrm{/}2=3.1416\cdot 1^2\mathrm{/}2\doteq 1.5708{\text{cm}}^2 \\ {S}_2={\displaystyle \frac{\sqrt{3}}{4}}\cdot a^2={\displaystyle \frac{\sqrt{3}}{4}}\cdot 2^2=\sqrt{3}{\text{cm}}^2\doteq 1.7321{\text{cm}}^2 \\ S=S_2-S_1=1.7321-1.5708=0.1613{\text{cm}}^2 \end{gathered}$$

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