Question 1205151
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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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<pre>
Let "r" be the radius of the circle.


The area of the circle is  {{{pi*r^2}}}.


The regular hexagon inscribed in the circle, consists of 6 regular triangles with the side length r.


The area of each such triangle is  {{{r^2*(sqrt(3)/4)}}};  the area of the regular hexagon is  

    {{{6*r^2*(sqrt(3)/4)}}} = {{{(3*r^2*sqrt(3))/2}}}.



The ratio  {{{area_of_the_hexagon/the_area_of_the_circle}}}  is  


    {{{((3*r^2*sqrt(3)/2))/(pi*r^2)}}} = {{{(3*sqrt(3))/(2*pi)}}} = 0.826994  (rounded).    <U>ANSWER</U>
</pre>

Solved.