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How many diagonals does a convex polygon of #n# sides have?

Answer 1

Number of diagonals of a convex polygon of #n# sides is #(n(n-3))/2#

Let there be a polygon ( I am assuming a convex polygon) of #n# sides.

Let us consider its one vertex. This does not form a diagonal with itself as well as immediate two neighbouring vertices,

hence it can for diagonals with remaining #(n-3)# vertices, #(n-3)# diagonals

Hence #n# vertices can form #n(n-3)# diagonals

but, as each diagonal has been counted twice, as it was counted as fresh diagonal when either of the vertices at its ends was considered, but actually we have only one diagonal.

Hence number of diagonals of a convex polygon of #n# sides is #(n(n-3))/2#

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Answer 2

Evelyn Arboleda

A convex polygon with ( n ) sides has (\frac{n(n-3)}{2}) diagonals.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.