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How many unique diagonals can be drawn in a five-sided convex polygon?

 Mar 22, 2015
 #1
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+5

Notice, that from each vertex, 2 diagonals can be drawn, giving us 10 diagonals. But the diagonal drawn from vertex A to vertex D would be the same diagonal drawn fro vertex D to vertex A.

So, we need to divide this by 2  = 5 diagonals.

Here's a pic to demonstrate this.....

pentstar.jpg (49409 bytes)

 

BTW....the number of diagonals that can be drawn in any regular polygon is given by....

[n*(n-3)] / 2     .... for n > 3

 

  

 Mar 22, 2015

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