Question 1205151: A regular hexagon is inscribed in a circle. Find the ratio of the area of the hexagon to the area of the circle. Answer by ikleyn(52813) (Show Source):
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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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Let "r" be the radius of the circle.
The area of the circle is .
The regular hexagon inscribed in the circle, consists of 6 regular triangles with the side length r.
The area of each such triangle is ; the area of the regular hexagon is
= .
The ratio is
= = 0.826994 (rounded). ANSWER
