document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190673>Question 1190673</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I want to make an octagon with all sides equal and all I have is a inside diameter. How can I figure this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822386 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822386\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A diagram....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-1%2C4%2C-1%2C4%0D%0A%2Cline%280%2C0%2C1%2C0%29%2Cline%281%2C0%2C1.707%2C.707%29%2Cline%281.707%2C.707%2C1.707%2C1.707%29%2Cline%281.707%2C1.707%2C1%2C2.414%29%2Cline%281%2C2.414%2C0%2C2.414%29%2Cline%280%2C2.414%2C-.707%2C1.707%29%2Cline%28-.707%2C1.707%2C-.707%2C.707%29%2Cline%28-.707%2C.707%2C0%2C0%29%0D%0A%2Clocate%280%2C-.1%2CA%29%2Clocate%28-.9%2C.8%2CB%29%2Clocate%28-.9%2C1.8%2CC%29%2Clocate%280%2C2.7%2CD%29%2Clocate+%281%2C2.7%2CE%29%0D%0A%2Cline%280%2C0%2C0%2C2.414%29%2Cline%280%2C0%2C1%2C2.414%29%2Cline%28-.707%2C1.707%2C0%2C1.707%29%2Cline%28-.707%2C.707%2C0%2C.707%29%0D%0A%2Clocate%28.1%2C1.8%2CP%29%2Clocate%28.1%2C.8%2CQ%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The information you have is the diameter of the octagon, which is AE in the diagram.  The objective (presumably) is to determine the length of the side of the octagon in terms of the length of the diagonal.<br><BR>\n" );
document.write( "We can solve the problem the other way around -- finding the length of the diagonal in terms of the length of a side of the octagon.<br><BR>\n" );
document.write( "For simplicity, we can let the side length of the octagon be 1.  So AB=BC=CD=DE=1; and PQ is also 1.<br><BR>\n" );
document.write( "Triangles AQB and CPD are 45-45-90 right triangles, so AQ=PD=sqrt(2)/2.<br><BR>\n" );
document.write( "Then in triangle ADE the legs are lengths <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the hypotenuse is the given diameter.<br><BR>\n" );
document.write( "Using the Pythagorean Theorem on that triangle...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2=1%5E2%2B%281%2Bsqrt%282%29%29%5E2 ALIGN=MIDDLE  ALT=\"d%5E2=1%5E2%2B%281%2Bsqrt%282%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use decimal approximations and a calculator gives us d=2.613 to 3 decimal places.<br><BR>\n" );
document.write( "So, given the diameter d, the side length of the octagon is d/2.613 = 0.383d.<br><BR>\n" );
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