document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57951>Question 57951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the formula for the number of diagonals in a polygon with  \"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 #39612 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=39612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Every two vertices determines a line.<BR>\n" );
document.write( "A polygon of n sides has n vertices.<BR>\n" );
document.write( "There are nC2=[n(n-1)]/2 lines determined.<BR>\n" );
document.write( "But n of the lines are sides of the polygon.<BR>\n" );
document.write( "So there are nC2 - n diagonals in an n-sided polygon.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "A pentagon has 5 vertices; it has 5C2 - 5 = [5*4]/2 - 5<BR>\n" );
document.write( "=10-5 = 5 diagonals.<BR>\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );