Math CentralQuandaries & Queries


Question from Sofia, a student:

What are diagonals and if you drew an octagon and drew all the diagonals how many would there be? Please explain because this is pretty confusing! Thank you!

Hi Sofia,

If you go to the Quandaries and Queries page on Math Central
and use the Quick Search to search for the term diagonal you will see number of questions we have received on diagonals of polygons. I am going to suggest 3 that you should look at. I suggest you look at them in the order I have given.

Julie's asked about the number of diagonals from one vertex of a 12 sided polygon. In Leeanna's response she defines a diagonal and answers Julie's question.

Karan asked about the number of diagonals in an 11 sided polygon (a hendecagon) and Penny leads Karan in a process to build on Leeanne's response above to answer her question.

Edna's question is about the number of diagonals in an $n$ sides polygon and Stephen takes an entirely different approach to answer her question.

If you want to extend Leeanne's and Penny's approach to a general formula you might want to look at our reply to Steven.

Let me know if you need any other assistance,

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