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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.


ABCDEF Is A Regular Hexagon, With O As The Centre. There Is ...


Options:
A .   20√3
B .   24√3
C .   18√3
D .   28√3
E .   118
Answer: Option B
:
B

The hexagon can be graphically divided as follows


ABCDEF Is A Regular Hexagon, With O As The Centre. There Is ...


Hence, there are totally 54 equilateral triangles out of which 24 are unshaded. Each of the triangles have a  side 2. Total unshaded area = √34 x 4 x 24 = 24√3


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