document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1113612>Question 1113612</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #728676 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=728676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  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? <BR>\n" );
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document.write( "Sketch the square<BR>\n" );
document.write( "Draw a line segment connecting the midpoints of the sides.<BR>\n" );
document.write( "Note: That line has length equal to the side of the square.<BR>\n" );
document.write( "Call it \"the center line\".<BR>\n" );
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document.write( "Sketch half of the dodecagon in the top half of the square<BR>\n" );
document.write( "Connect each of the six vertices to the center of the square<BR>\n" );
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document.write( "Note:: 360/12 = 30 degrees<BR>\n" );
document.write( "Note: You have 6 triangles in the top half of the square<BR>\n" );
document.write( "Note: The base of each of the triangles has length 2<BR>\n" );
document.write( "Note: Using the triangle on \"the center line::<BR>\n" );
document.write( "Draw a perpendicular bisector of its base.<BR>\n" );
document.write( "That forms a right triangle with base = 1, central angle = 15 degrees,<BR>\n" );
document.write( "and hypotenuse = (1/2) the side of the square = \"r\"<BR>\n" );
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document.write( "Then sin(15 deg) = 1/r<BR>\n" );
document.write( "r = 1/sin(15) = 3.864<BR>\n" );
document.write( "Then side of square = 2*3.864 = 7.727<BR>\n" );
document.write( "Ans : Area of the square = 59.71 sq.units<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "-- </SPAN>\n" );
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