question_answer

An equilateral triangle of side 6 cm has its comers cut off to arm. a regular hexagon. Area (in\[c{{m}^{2}}\]) of this regular hexagon will be

A)  \[3\sqrt{3}\]     

B)  \[3\sqrt{6}\]

C)  \[6\sqrt{3}\]     

D)  \[\frac{5\sqrt{6}}{2}\]

Correct Answer: C

Solution :

[c] \[=\frac{1}{3}\times 6=2\,\,cm\] \[\therefore \]Area of the hexagon \[=\frac{3\sqrt{3}}{2}{{a}^{2}}\] \[=\frac{3\sqrt{3}}{2}\times 2\times 2=6\sqrt{3}\,\,sq.cm.\]