Question

ABCDEF is a regular hexagon, with O as the centre. There is another regular hexagon with two 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 $FP=\frac{1}{3}FO$.

• A. 24
• B. 24√3
• C. 70
• D. 82

Answer 1

The correct option is B

24√3

Hence, there are totally 54 equilateral triangles out of which 24 are unshaded. Each of the triangles have a side 2.
Total unshaded area = $\frac{\sqrt{3}}{4}\times 4\times 24=24\sqrt{3}$.