SOLUTION: A regular hexagon is inscribed in a circle. Find the ratio of the area of the hexagon to the area of the circle. https://ibb.co/gyKHVbS

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Question 1209087: A regular hexagon is inscribed in a circle. Find the ratio of the area of the hexagon to the area of the circle.
https://ibb.co/gyKHVbS
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

Let r be the radius of the circle.


The area of the circle is  .


The regular hexagon consists of 6 equilateral triangles with the side length of r.

The area of each such a triangle is  ;

hence, the area of the regular hexagon is   = .


Thus the ratio of the area of the hexagon to that of the circle is

     = 0.827 (rounded).    ANSWER

Solved.




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