# Need some help understanding what this question is asking.

• Dec 1st 2011, 10:42 AM
Need some help understanding what this question is asking.
The question is as follows:

"A diagonal is a line connecting any 2 points in a polygon. How many diagonals are there in a heptagon?

If the question really means ANY two points then isn't there an infinite number of diagonals? Or if there is a equation to solve this, I certainly haven't learned it. Since this unit is trying to teach applications of permutations and combinations, I'm assuming the question is really only asking about the corner points in which case wouldn't the question be solved by $\displaystyle _{7}C_{2}$?
• Dec 1st 2011, 11:05 AM
emakarov
Re: Need some help understanding what this question is asking.
Quote:

"A diagonal is a line connecting any 2 points in a polygon. How many diagonals are there in a heptagon?

If the question really means ANY two points then isn't there an infinite number of diagonals?

I agree, this definition of a diagonal seems sloppy. Wikipedia and MathWorld define a diagonal as a line segment joining two nonadjacent vertices of a polygon.

Quote:

Since this unit is trying to teach applications of permutations and combinations, I'm assuming the question is really only asking about the corner points in which case wouldn't the question be solved by $\displaystyle _{7}C_{2}$?

Yes, if you include the sides, i.e., segment joining adjacent vertices. Otherwise, the answer is $\displaystyle \frac{7\cdot 4}{2}$.
• Dec 1st 2011, 05:11 PM
mathland
Re: Need some help understanding what this question is asking.
We can also use the formula (n/2)(n - 3) noting that a heptagon is a polygon having 7 sides. So, let n = 7 and simplify.

(n/2)(n - 3) =

Let n = 7

(7/2)(7 - 3) =

(7/2)(4) =

(7)(2) = 14 diagonals.