document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #841799 by ikleyn(52817)\"\" \"About 
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\n" ); document.write( "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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document.write( "Let \"r\" be the radius of the circle.\r\n" );
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document.write( "The area of the circle is  \"pi%2Ar%5E2\".\r\n" );
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document.write( "The regular hexagon inscribed in the circle, consists of 6 regular triangles with the side length r.\r\n" );
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document.write( "The area of each such triangle is  \"r%5E2%2A%28sqrt%283%29%2F4%29\";  the area of the regular hexagon is  \r\n" );
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document.write( "    \"6%2Ar%5E2%2A%28sqrt%283%29%2F4%29\" = \"%283%2Ar%5E2%2Asqrt%283%29%29%2F2\".\r\n" );
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document.write( "The ratio  \"area_of_the_hexagon%2Fthe_area_of_the_circle\"  is  \r\n" );
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document.write( "    \"%28%283%2Ar%5E2%2Asqrt%283%29%2F2%29%29%2F%28pi%2Ar%5E2%29\" = \"%283%2Asqrt%283%29%29%2F%282%2Api%29\" = 0.826994  (rounded).    ANSWER\r\n" );
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