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: Option B
Explanation
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 6sqrt{3}}{2 times 2})
= (54 sqrt{3})cm2