document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104011>Question 1104011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square with the side length of x has all four corners cut off, forming a regular octagon. Derive the area of the octagon. </SPAN>\n" );
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document.write( "Let s be the side length of the regular octagon that is formed.  Then the 4 corners that are cut off of the original square can be put together to form a square of side length s; so the area of the 4 corners cut off is s^2; so the area of the octagon is x^2-s^2.<br><BR>\n" );
document.write( "To find the relationship between s and x, observe that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+s%2Fsqrt%282%29%2Bs%2Bs%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+s%2Fsqrt%282%29%2Bs%2Bs%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+s%28sqrt%282%29%2B1%29 ALIGN=MIDDLE  ALT=\"x+=+s%28sqrt%282%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+x%2F%28sqrt%282%29%2B1%29+=+x%2A%28sqrt%282%29-1%29 ALIGN=MIDDLE  ALT=\"s+=+x%2F%28sqrt%282%29%2B1%29+=+x%2A%28sqrt%282%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the area of the octagon is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-s%5E2+=+x%5E2+-+%28x%2A%28sqrt%282%29-1%29%29%5E2+=+x%5E2+-+x%5E2%283-2%2Asqrt%282%29%29+=+x%5E2-3x%5E2%2B2x%5E2%2Asqrt%282%29+=+x%5E2%282%2Asqrt%282%29-2%29+=+2x%5E2%28sqrt%282%29-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );