740
The number of digaonals is given by n(n-3)/2, where n is the number of sides (or vertices) of a polygon:
40(40-3)/2=20*37=740
For a proof, see:
http://www.artofproblemsolving.com/Wiki/index.php/Diagonal
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The sum of the angles of a regular n-sided polygon is equal to (n - 2) x 180 degrees.Therefore, the sum of the angles of a regular 40-sided polygon (tetradecagon) is equal to (40 - 2) x 180 = 6840 degrees. Therefore, 6840 refers to the sum of the degrees, not the number of diagonals.The number of diagonals of an n-sided polygon is given by n(n-3)/2. So a 40-sided polygon has 40*37/2=740 diagonals.
tetracontahedron
40-gon.
I find the name "30-sided polygon", "40-sided polygon", etc. just fine.
A 40 sided polygon is call a Tetracontagon. Try saying that ten times fast. :) Hope this helped.