Multiple choice

If a regular hexagon is inscribed in a circle of radius $r$, then find the distance between the parallel sides.

  1. $\sqrt {3}r$
  2. $6r$
  3. $3r$
  4. $12r$
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A Correct answer
Explanation

In a regular hexagon inscribed in a circle of radius r, the distance between parallel sides is twice the apothem. The apothem is r * cos(30) = r * sqrt(3)/2. Distance = 2 * (r * sqrt(3)/2) = r * sqrt(3).

AI explanation

A regular hexagon inscribed in a circle has sides equal to the radius, so the distance between opposite parallel sides is twice the length of the apothem. The apothem of a regular hexagon is found using the formula r times the square root of 3 divided by 2, where r is the radius. Therefore, twice the apothem equals r times the square root of 3, meaning the distance is the square root of 3 times r.

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