sud21 wrote:
Angle AOB = 360/6 = 60º
OA = OB = 6, so triangle OAB is an isosceles triangle, which implies angle OAB = angle OBA. This means all three angles of the triangle OAB are equal. So, OA = OB = AB = 6, which is an equilateral triangle.
Area of an equilateral triangle = a²√3/4
So, area of one equilateral triangle = 6² * √3/4 = 36√3/4 = 9√3
Therefore, area of 6 equilateral triangles or area of hexagon = 6 * 9√3 = 54√3
Area of circle = (pi) * (radius)² = (pi) * 6² = 36(pi)
Hence, required value = 36(pi) - 54√3, which is the same as [spoiler](C)[/spoiler].
The correct answer is C.
