Multiple choice

A regular hexagon is inscribed in a circle of radius $6$ cm. Find its area (in cm$\displaystyle^{2}$).

  1. $\displaystyle 48\sqrt{3}$
  2. $\displaystyle 54\sqrt{3}$
  3. $\displaystyle 48\sqrt{2}$
  4. $\displaystyle 54\sqrt{2}$
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B Correct answer
Explanation

A regular hexagon inscribed in a circle of radius r consists of 6 equilateral triangles with side length r. Area = 6 * (sqrt(3)/4) * r^2. With r=6, Area = 6 * (sqrt(3)/4) * 36 = 54 * sqrt(3).

AI explanation

A regular hexagon inscribed in a circle is divided into six equilateral triangles, each with a side length equal to the radius of the circle. Using the area formula for an equilateral triangle, (sqrt(3) / 4) * side^2, the area of one triangle is (sqrt(3) / 4) * 6^2 = 9 sqrt(3) cm^2. Multiplying this by the six triangles gives a total area of 54 sqrt(3) cm^2. The area of the regular hexagon is 54 sqrt(3).

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