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

Mathematics
JAMB 1978

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

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

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


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