document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153292>Question 1153292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the area of the regular octagon circumscribing a circle having an area of 126 m2.<BR>\n" );
document.write( "A. 127.83 m2 <BR>\n" );
document.write( "B. 132.90 m2<BR>\n" );
document.write( "C. 119.05 m2 <BR>\n" );
document.write( "D. 113.44 m2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #775496 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=775496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw this<BR>\n" );
document.write( "The area of the circle is 126 m^2=pi*r^2<BR>\n" );
document.write( "therefore, r=6.333<BR>\n" );
document.write( "Each of the 8 parts of the octagon is a triangle with central angle 45 deg<BR>\n" );
document.write( "Draw a perpendicular to the side, and this bisects the central angle.<BR>\n" );
document.write( "That triangle has angle 22.5, the opposite side is half the length of a side of the octagon, and the perpendicular line is the adjacent side.\r<BR>\n" );
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document.write( "cos22.5=adj/6.333; adj side =5.851<BR>\n" );
document.write( "sin 22.5=opp/6.333, opp side=2.424\r<BR>\n" );
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document.write( "the side of the octagon is 4.848, double the above for sin 22.5<BR>\n" );
document.write( "the altitude is 5.851<BR>\n" );
document.write( "1/2 that product is the area of the triangle.<BR>\n" );
document.write( "There are 8 such triangles, so 4 times the product is the answer or 113.46 m^2.<BR>\n" );
document.write( "D.<BR>\n" );
document.write( " </SPAN>\n" );
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