SOLUTION: A regular hexagon is inscribed in a circle. Find the ratio of the area of the hexagon to the area of the circle.
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-> 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(52793) (Show Source):
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
