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A regular hexagon is inscribed in a circle of radius 6 cm. Its area is:

Competition practiceTrigonometry
  • A27√
  • B108√
  • C36√
  • D54√

Step-by-Step Solution

The six radii cut the hexagon into six triangles, each with two sides of 6 cm and an included angle of 360°/6 = 60°. Each has area ·sin60° = 9√3, so the hexagon is √3 = 54√3 ≈ . Forgetting the (1/2) in the area formula doubles it to 108√3.
Answer: D) 54√

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