# 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 =  0.161 cm2

#### Solution:

$a=2 \ \text{cm} \ \\ r=1 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r^2 /2=3.1416 \cdot \ 1^2 /2 \doteq 1.5708 \ \text{cm}^2 \ \\ \ \\ S_{2}=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ a^2=\dfrac{ \sqrt{ 3 } }{ 4 } \cdot \ 2^2 \doteq \sqrt{ 3 } \ \text{cm}^2 \doteq 1.7321 \ \text{cm}^2 \ \\ \ \\ S=S_{2}-S_{1}=1.7321-1.5708=0.161 \ \text{cm}^2$

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