document.write( "Question 1113612: So I have this dodecagon with the side length of 2, it is inscribed in a square. How do i find the area of the square with only that information? \n" ); document.write( "

Algebra.Com's Answer #728681 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Go to Wikipedia and look in this its article https://en.wikipedia.org/wiki/Dodecagon \r\n" );
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document.write( "talking about dodecagon (it is better one time to see than 100 times to hear).\r\n" );
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document.write( "Dodecagon has 12 sides. We consider a REGULAR dodecagon.\r\n" );
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document.write( "Look in the figure in this article.\r\n" );
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document.write( "In my solution, I consider the scheme when 4 vertices of the regular dodecagon coincide with the midpoints of square sides.\r\n" );
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document.write( "I will work with 3 sides of the regular dodecagon that are located in QIII.\r\n" );
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document.write( "These three sides are sloped at 15°, 45° and 75° to the horizontal line.\r\n" );
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document.write( "The sides are of 2 units long each.\r\n" );
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document.write( "It means that half of the square side length is this sum\r\n" );
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document.write( " = 2*cos(15°) + 2*cos(45°) + 2*cos(75°) =  = 3.866.\r\n" );
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document.write( "Hence, the square side length = 2*3.866 = 7.731.\r\n" );
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document.write( "Then the square area =  =  = 59.772.\r\n" );
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document.write( "Answer.  The square area = 59.772 square units (approximately).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice that in his solution @greneestamps considers different scheme of the regular dodecagon inscribed to the square.\r
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