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Distinct Diagonals Of A Regular Polygon:

A.  The number of distinct diagonals of a regular n-agon is determined by the following formula:

(n-2) triangular number - 1

B.  See Triangular Numbers.

C.  Examples

Ex [1]  The number of distinct diagonals of a regular pentagon is _______.

a.  Since "penta" means 5, we need the 3^rd triangular number minus 1.

b.  The 3^rd triangular number is 6. 6-1=5.

c.  The answer is 5.

Ex [2]  The number of distinct diagonals of a regular decagon is ______.

a.  Since "deca" means 10, we need the 8^th triangular number minus 1.

b.  The 8^th triangular number is 36.  36-1=35.

c.  The answer is 35.

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