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There are 9 diagonals in every hexagon.


To see why, select any one of the 6 vertices. There are 5 other vertices to which it can be joined. But the lines joining it to the two adjacent vertices (one on each side) are not diagonals but sides of the hexagon. So, from each vertex, you get 3 diagonals.


The first vertex can be selected in 6 ways so it would seem that you have 6*3 = 18 diagonals. However, you will then be counting each diagonal twice: once from each end. So the correct answer is 18/2 = 9.


In general, a polygon with n sides has n*(n-3)/2 diagonals. Also, whether or not it is regular is totally irrelevant.

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9y ago

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