Number of diagonals in convex polygon : GMAT

October 24, 2009 By K S Baskar 1 Comment

Any n-sided convex polygon with more than 3 sides will have n(n-3)/2 diagonals.

For instance, let us look at a square. A square has 4 sides and 2 diagonals. Let us apply this formula with n = 4.

We get 4(4-3)/2 = 2 diagonals.

Here is a question on finding the number of diagonals.

If a n-sided convex polygon has 14 diagonals, how many sides does the polygon have?

Any n-sided convex polygon has n(n-3)/2 diagonals.
This polygon has 14 diagonals.
i.e., n(n-3)/2 = 14
Or n(n-3) = 28
Solving for n, we get n = 7.

So, the given polygon has 7 sides.

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