document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54170>Question 54170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many diagonals does a 30-sided polygon have?<BR>\n" );
document.write( "How do you find a formula to solve this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #36446 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=36446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How many diagonals does a 30-sided polygon have?<BR>\n" );
document.write( "How do you find a formula to solve this?<BR>\n" );
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document.write( "If you know something about combinations the number<BR>\n" );
document.write( "of pairs of points is 30C2=[30)(29)/2]=15(29)=435<BR>\n" );
document.write( "But 30 of those pairs form the sides of the polygon<BR>\n" );
document.write( "So the # of diagonals is 435-30=405<BR>\n" );
document.write( "Try this on smaller polygons. <BR>\n" );
document.write( "For example how about a pentagon<BR>\n" );
document.write( "5C2-5 = [5*4/2]-5 sides = 10-5=5 diagonals<BR>\n" );
document.write( "A formula would look like nC2 - n = [(n)(n-1)/2 -n] or (n^2-3n)/2<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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