Multiple choice

Which of the following is the perimeter of a regular hexagon inscribed in a circle of radius r?

  1. 2r

  2. 5r

  3. 6r

  4. 9r

  5. 12r
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A regular hexagon inscribed in a circle of radius r has sides equal to the radius r. The perimeter is 6 * r.

AI explanation

A regular hexagon inscribed in a circle is made of six equilateral triangles, each with a side length equal to the radius r. To see this, connect the center of the circle to each of the six vertices of the hexagon, creating six isosceles triangles with two sides of length r and a vertex angle of 60 degrees. Since two sides are equal and the included angle is 60 degrees, all three angles are 60 degrees, making each triangle equilateral. The perimeter of the hexagon is the sum of its six sides, so multiplying the side length r by 6 gives 6r.

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