Question 1209087
.
<pre>

Let r be the radius of the circle.


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


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

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

hence, the area of the regular hexagon is  {{{6r^2*(sqrt(3)/4)}}} = {{{3r^2*(sqrt(3)/2)}}}.


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

    {{{(3*sqrt(3))/(2*pi)}}} = 0.827 (rounded).    <U>ANSWER</U>
</pre>

Solved.