ABCDEF is a regular hexagon, with O as the centre. There is another regular hexagon with 2 of the end points PQ inscribed in the above hexagon (again with centre O). Find the area of the unshaded region, given that FPQC lies on a straight line and FP=CQ=2 and FP =13 FO.
Options:
A .  20√3
B .  24√3
C .  18√3
D .  28√3
Answer: Option B : B The hexagon can be graphically divided as follows Hence, there are totally 54 equilateral triangles out of which 24 are unshaded. Each of the triangles have aside 2. Total unshaded area = √34 x 4 x 24 = 24√3
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