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.

Result

S =  0.161 cm2

Solution:

a=2 cm r=1 cm  S1=π⋅ r2/2=3.1416⋅ 12/2≐1.5708 cm2  S2=34⋅ a2=34⋅ 22=3 cm2≐1.7321 cm2  S=S2−S1=1.7321−1.5708≐0.1613=0.161 cm2a = 2 \ cm \ \\ r = 1 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 /2 = 3.1416 \cdot \ 1^2 /2 \doteq 1.5708 \ cm^2 \ \\ \ \\ S_{ 2 } = \dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2 = \dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 2^2 = \sqrt{ 3 } \ cm^2 \doteq 1.7321 \ cm^2 \ \\ \ \\ S = S_{ 2 }-S_{ 1 } = 1.7321-1.5708 \doteq 0.1613 = 0.161 \ cm^2

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Pythagorean theorem is the base for the right triangle calculator.
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