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      Question

      ABCDEF is a regular hexagon, and m(AD) = 12 cm. What is

      the area (in cm²) of the given hexagon?
      A 216√3 cm² Correct Answer Incorrect Answer
      B 108√3 cm² Correct Answer Incorrect Answer
      C 162√3 cm² Correct Answer Incorrect Answer
      D 54√3 cm² Correct Answer Incorrect Answer

      Solution

      ATQ, Let Understand what AD is

      In a regular hexagon, opposite vertices are 2 side lengths apart in a straight line through the center. So A and D are opposite vertices. That means AD is the "diameter" of the hexagon. So, In a regular hexagon, side length s = radius of the circumscribed circle. Distance between opposite vertices = 2s. So: AD = 2s 12 = 2s s = 6 cm Area formula Area of a regular hexagon with side length s is: Area = (3√3 / 2) · s² Plug in s = 6: s² = 36 Area = (3√3 / 2) · 36  = 54√3 cm²

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