Star Stumper

Geometry Level 4

A square ABCDABCD of side length 22 has a 4-pointed star inscribed in it - its points touch the midpoints of each side of the square, and it has lines of symmetry ACAC and BDBD.

Given that the angle between the points is 120120^\circ , the area of the shaded region can be written as ab3c\dfrac { a-b\sqrt { 3 } }{ c } where aa, bb and cc are coprime. Find a+b+ca+b+c.

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