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Problem Solving (PS) | Arcs AC, AB and BC are centered at B, C and A respectively, as shown a

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reto wrote:


Arcs AC, AB and BC are centered at B, C and A respectively, as shown above. If the area of equilateral triangle ABC is √3, what is the area of the shaded region?

A. \(2pi-3\sqrt{3}\)
B. \(\sqrt{3} - pi\)
C. 3pi
D. \(\sqrt{3}+2pi\)
E. 3

1) Choose one vertex and its segment, say B

2) Area of shaded region for B:
(Area of segment) - (Area of triangle)

3) Segment area - find SIDE LENGTH of equilateral triangle, which is the RADIUS of Circle B:

Find side length
Area of equilateral triangle,
...

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