document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120973>Question 1120973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of a regular octagon inscribed in a circle woth radius r\r<BR>\n" );
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document.write( "Hint: A regular octagon consists of eight isosceles triangles that have the same shape and size </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736699 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=736699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 360/8 means the central angle of each triangle is 45 degrees.  With the radius on each side being r, the other two angles are equal and each of the 8 triangles is isosceles, with angles 67.5 degrees.  <BR>\n" );
document.write( "The triangle can be split into two right triangles, each with angles 22.5, 67.5 and 90 degrees.  The dividing line has length cos 22.5=x/r so length is r cos 22.5 or 0.9239 r.\r<BR>\n" );
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document.write( "Half the length is the base of the right triangle, whose length is r sin 22.5 or 0.3827 r.  The whole base of one of the eight triangles is twice that or 0.7654.\r<BR>\n" );
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document.write( "The area of each of the 8 triangles =(1/2)bh, or 0.7654*0.9239*.5*r^2 or 0.3536 r^2\r<BR>\n" );
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document.write( "Eight of them, the answer, is 2.83 r^2 </SPAN>\n" );
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