document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=554031>Question 554031</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you to find the length of a side of a octagon with only the measurement of the total area(35cm^2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #361174 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=361174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how do you to find the length of a side of a octagon with only the measurement of the total area(35cm^2)<BR>\n" );
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document.write( "If it's a regular octagon, it's comprised of 8 isoceles triangles having vertex angles of 45 degs, each with an area of 35/8 sq cm.<BR>\n" );
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document.write( "b = length of sides<BR>\n" );
document.write( "h = height of triangle (the apothem of the octagon)<BR>\n" );
document.write( "(b/2)/h = tan(22.5)<BR>\n" );
document.write( "b = 2h*tan(22.5)<BR>\n" );
document.write( "h = (b/2)*cot(22.5)<BR>\n" );
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document.write( "b*h/2 = 35/8 (Area of 1 triangle)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E2%2F2%29%2Acot%2822.5%29+=+35%2F8 ALIGN=MIDDLE  ALT=\"%28b%5E2%2F2%29%2Acot%2822.5%29+=+35%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+sqrt%2835%2Atan%2822.5%29%2F4%29 ALIGN=MIDDLE  ALT=\"b+=+sqrt%2835%2Atan%2822.5%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b =~ 1.904 cm<BR>\n" );
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document.write( "You can use the formula for area of a polygon with n sides of length s:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=+ns%5E2%2Acot%28180%2Fn%29%2F4 ALIGN=MIDDLE  ALT=\"Area+=+ns%5E2%2Acot%28180%2Fn%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Applies to all regular polygons </SPAN>\n" );
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