SOLUTION: A regular hexagon is inscribed into a circle. Find the perimeter of the hexagon, if the diameter of the circle is 12?

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Question 1143868: A regular hexagon is inscribed into a circle. Find the perimeter of the hexagon, if the diameter of the circle is 12?
Answer by ikleyn(52781) About Me  (Show Source):
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Connect the center of the hexagon with its vertices by segments.


You will get 6 isosceles triangles (since the lateral sides of each triangle have equal lengths).


The central angle of each triangle is 60 degrees -- so all these triangles are equilateral.


Therefore, the perimeter of the hexagon is 6 times the radius  


    Perimeter = 6*6 units = 36 units.    ANSWER