ABCDEF is a regular hexagon, with O as the centre. There is another regular hexa

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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 =

\frac{1}{3}

FO.

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

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 aside 2. Total unshaded area =

\frac{\sqrt{3}}{4}

x 4 x 24 = 24

\sqrt{3}

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