A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is

A.

36\(\pi\)cm2

B.

54\(\sqrt{3}\)cm2

C.

\(\sqrt{3}\)cm2

D.

\(\frac{1}{x - 1}\)

Correct answer is B

Sum of interior angle of hexagon = [2(6) - 4]90°

= 720°

sum of central angle = 360°

Each central angle = \(\frac{360}{6}\)

= 60°

Area of Hexagon = \(\frac{1}{2}\) x 6 x 6 sin 60°

\(\frac{36 \times 6\sqrt{3}}{2 \times 2}\)

= \(54 \sqrt{3}\)cm2