Eq triangle minus arcs

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

Final Answer:

S =  0.1613 cm²

Step-by-step explanation:

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

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