document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209920>Question 1209920</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It has been done before on this website but the question was wrong:\r<BR>\n" );
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document.write( "Two identical squares with side of (1+sqrt(2))m overlap to form a regular octagon. What is the area of the octagon? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851053 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=851053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "When the two squares overlap to form a regular octagon, the regions inside the squares and outside the octagon are eight isosceles right triangles.<br><BR>\n" );
document.write( "Let x be the side length of each of those triangles; then x*sqrt(2) is the length of the hypotenuse, which is the side length of the octagon.<br><BR>\n" );
document.write( "The side length of each square is then 2x+x*sqrt(2).  Since the side length of the square is 1+sqrt(2),<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Bx%2Asqrt%282%29=1%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"2x%2Bx%2Asqrt%282%29=1%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%282%2Bsqrt%282%29%29=1%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"x%282%2Bsqrt%282%29%29=1%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%281%2Bsqrt%282%29%29%2F%282%2Bsqrt%282%29%29=%28%281%2Bsqrt%282%29%29%282-sqrt%282%29%29%29%2F%28%282%2Bsqrt%282%29%29%282-sqrt%282%29%29%29=sqrt%282%29%2F2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The side length of the octagon, x*sqrt(2), is then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29%2F2%29%28sqrt%282%29%29=1 ALIGN=MIDDLE  ALT=\"%28sqrt%282%29%2F2%29%28sqrt%282%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The area of a regular octagon with side length s is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2s%5E2%281%2Bsqrt%282%29%29 ALIGN=MIDDLE  ALT=\"A=2s%5E2%281%2Bsqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The side length of our octagon is 1, so the area is<br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%281%2Bsqrt%282%29%29 ALIGN=MIDDLE  ALT=\"2%281%2Bsqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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