A regular hexagon is inscribed in a circle with a radius of 42 cm, find its perimeter.

univerkov | September 16, 2021 | education

In the hexagon, draw large diagonals that divide the hexagon into six isosceles triangles.

The degree measure of the circle is 360, then the hexagon divides the circle into six equal arcs. Arc AC = 360/6 = 60, then the central angle of the AOC triangle is also 60, and therefore the AOC triangle is equilateral, OA = OC = AC = R = 42 cm.

Then the perimeter of the hexagon is: P = 6 * AC = 6 * 42 = 252 cm.

Answer: The perimeter of the hexagon is 252 cm.

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