True or False: A polygon of 7 sides (septagon or heptagon) has C (7,2) diagonals.

Question

anonymous · Answer

True I guess

directrix · Answer

If C(7,2) is the number of segments determined by the 7 vertices of the 7-gon, would EVERY segment determined be a diagonal?

anonymous · Answer

Not your answer I know but 7-sides=Heptagon.

directrix · Answer

I included that in the question:

True or False: A polygon of 7 sides (septagon or heptagon) has C (7,2) diagonals

mertsj · Answer

False.  It has 14

directrix · Answer

A polygon of 7 sides (septagon or heptagon) has C (7,2) diagonals is false.

because C (7,2) includes ALL possible segment determined by taking 7 points 2 at the time. Therefore, the 7 sides of the 7-gon have been included.

directrix · Answer

A polygon of 7 sides (septagon or heptagon) has C (7,2) - 7 diagonals.

This result can be generalized to a formula for the number of diagonals of a convex n-gon. The number is [ C(n,2) - n ]. There are other formulas but this one is, for me, easy to remember.

Others may prefer the [n(n-3) ] / 2 formula.