document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266167>Question 266167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is an algebraic expression for the number of diagonals in any polygon of n sides? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195597 by </B><A HREF=/tutors/aboutme.mpl?userid=palanisamy><B>palanisamy(496)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=palanisamy><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=195597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A polygon has n sides and n vertices.<BR>\n" );
document.write( "A diagonal is obtained by joining two vertices.<BR>\n" );
document.write( "Total number = nC2 = n*(n-1)/2<BR>\n" );
document.write( "But this includes the n sides also.<BR>\n" );
document.write( "So the number of diagonals = n*(n-1)/2 -n<BR>\n" );
document.write( "                           =[n*(n-1)-2n]/2<BR>\n" );
document.write( "                           = n*(n-1-2)<BR>\n" );
document.write( "                           = n(n-3)/2 </SPAN>\n" );
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