document.write( "Question 927882: A square having an area of 48 m2 is inscribed in a circle which is inscribed in a regular hexagon. Compute the a. area of the circle, b. area of the regular hexagon and c. perimeter of the regular hexagon. \n" ); document.write( "

Algebra.Com's Answer #563613 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "The area of the square is 48 m² \r\n" );
document.write( "So a side of the square is √48 = √16×3 = 4√3 \r\n" );
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document.write( "AB is half a side of the square, so it's 2√3\r\n" );
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document.write( "OA is also 2√3\r\n" );
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document.write( "So by the Pythagorean theorem hypotenuse OB of right triangle OAB is\r\n" );
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document.write( "OB is the raius of the circle so by that formula for a circle's area:\r\n" );
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document.write( "Angle BDO is half of an interior angle of a regular hexagon. An\r\n" );
document.write( "interior angle of a regular hexagon is given by:\r\n" );
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document.write( "So angle BDO is 60°, so right triangle BDO is a 30°-60°-90°,\r\n" );
document.write( "so its hypotenuse OD is twice BD.  So by the Pythagorean theorem\r\n" );
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document.write( "BD is half a side of the hexagon, so one side of the\r\n" );
document.write( "hgecagon is , so the perimeter of the\r\n" );
document.write( "hexagon is 6 times that, or \r\n" );
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document.write( "Edwin

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