document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006573>Question 1006573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the lengths of the apothem and the radius of a square whose sides have length 10in ?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622678 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=622678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For any square, the apothem is always half as long as the side length\r<BR>\n" );
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document.write( "apothem = (1/2)*(side length)<BR>\n" );
document.write( "apothem = (1/2)*(10)<BR>\n" );
document.write( "apothem = 5\r<BR>\n" );
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document.write( "The apothem is 5 units long. The apothem is the segment starting at the center of the regular polygon and it stretches to the midpoint of any side of the regular polygon.\r<BR>\n" );
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document.write( "If you draw out the square, add in the apothem and radius, you'll see a right triangle form.\r<BR>\n" );
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document.write( "This right triangle has legs of 5 and 5. The hypotenuse is unknown. Let's call it x for now\r<BR>\n" );
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document.write( "Pythagorean theorem:<BR>\n" );
document.write( "a^2 + b^2 = c^2<BR>\n" );
document.write( "5^2 + 5^2 = x^2<BR>\n" );
document.write( "25 + 25 = x^2<BR>\n" );
document.write( "50 = x^2<BR>\n" );
document.write( "x^2 = 50<BR>\n" );
document.write( "x = sqrt(50)<BR>\n" );
document.write( "x = sqrt(25*2)<BR>\n" );
document.write( "x = sqrt(25)*sqrt(2)<BR>\n" );
document.write( "x = 5*sqrt(2)\r<BR>\n" );
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document.write( "So the radius of the square is 5*sqrt(2)<BR>\n" );
document.write( "The radius of a regular polygon (aka the circumradius) is the segment going from the center to any vertex of the regular polygon.\r<BR>\n" );
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document.write( "Answers:\r<BR>\n" );
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document.write( "Apothem = 5 inches<BR>\n" );
document.write( "(circum)radius = 5*sqrt(2) inches </SPAN>\n" );
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