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
\(\frac{1}{x - 1}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Sum of interior angle of hexagon = [2(6) - 4]90o
= 720o
sum of central angle = 360o
Each central angle = \(\frac{360}{6}\)
= 60o
Area of Hexagon = \(\frac{1}{2}\) x 6 x 6 sin 60o
\(\frac{36 \times 6\sqrt{3}}{2 \times 2}\)
= \(54 \sqrt{3}\)cm2
Source: Myschool Past Questions Archive (Record #32710)