Tetrakaiicosagon with Diagonals

Tetrakaiicosagon with Diagonals

How many diagonals does a polygon with 24 sides have?

First, consider that there are 24 vertices for diagonals to come from, and they each have 21 places to go, since they can’t go to themselves, or to the adjacent vertices. (24)(21) therefore equals twice the number of diagonals, since I just counted each one twice (once per endpoint). There are therefore (24)(21)/2 = 252 diagonals.

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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