document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192034>Question 1192034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the total number of diagonals for a polygon of n sides for the following values of n.<BR>\n" );
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document.write( "n = 7 </SPAN>\n" );
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document.write( "Consider a polygon with n sides.<BR>\n" );
document.write( "This means we have n vertices.\r<BR>\n" );
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document.write( "Each of the n vertices connects to n-3 diagonals<BR>\n" );
document.write( "The -3 is to exclude the two surrounding neighbors (which don't form diagonals but rather exterior sides), and the vertex itself.\r<BR>\n" );
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document.write( "There are n(n-3)/2 total diagonals.<BR>\n" );
document.write( "The dividing by 2 aspect is to avoid double-counting<BR>\n" );
document.write( "Eg: diagonal AC is the same as diagonal CA.\r<BR>\n" );
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document.write( "Plug in n = 7 to find that,<BR>\n" );
document.write( "n(n-3)/2 = 7*(7-3)/2 = 7*4/2 = 28/2 = 14\r<BR>\n" );
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document.write( "Answer: 14 diagonals in a heptagon.<BR>\n" );
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