A diagnal of a polygon is a degment joining the two nonconecutive vertcies of the polygon.How many dianals does a regular octagon have?

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- Dec 19th 2006, 03:47 PMRimasPetagons
A diagnal of a polygon is a degment joining the two nonconecutive vertcies of the polygon.How many dianals does a regular octagon have?

- Dec 19th 2006, 03:50 PMOReilly
- Dec 19th 2006, 03:51 PMAfterShock
We know that the octagon has exactly 8 vertices. We are then able to create 5 diagonals from a given vertex.

8*5 = 40; however, there are some repeats. Each diagonal is counted twice since there are 2 points to each diagonal. Thus, 40/2 = 20 is the number of diagonals in a regular octagon. - Dec 19th 2006, 03:55 PMOReilly
General formula for counting number of diagonals for any polygon is:

$\displaystyle D_n = \frac{{n(n - 3)}}{2}$

where $\displaystyle n$ is number of sides.