How many diagonals are there in an 11-sided figure?

Question

I know there's a formular to solve this prob. but I just forget it, too bad....

NO NO it's 44 but don't know how...

Answer 1

There are 88 or 44 depending on how you define what a unique diagonal is. ( Sorry, not trying to be "egghead-y" here, just trying to give you a complete explanation )

ANSWER OF 88:

Let's look at an n-sided figure. For each point (where two sides meet), you can't draw a diagonal from the point to the same point itself, nor from the point to the two points next to it on either side. But, you can draw a diagonal to every other point, or to n-3 points. You can do this for each of the n points.

So, in an n-sided figure, you can have n(n-3) diagonals.

So, in an 11-sided figure, you can have 11(11-3) diagonals = 11*8 diagonals = 88 diagonals.

Notice this answer assumes that the diagonal from point A to point B is different than the diagonal from point B to point A!

ANSWER OF 44:

To eliminate such "duplicates", we need to look at it this way for an n-sided figure:

Point 1 has n-3 diagonals (same reasoning as above)
Point 2 has n-3 diagonals (same reasoning as above)
Point 3 has n-4 diagonals (since 1 of its diagonals was already counted under Point 1)
Point 4 has n-5 diagonals (since 2 of its diagonals have already been counted)
... etc ... till we get to ....
Point n-2 has 1 diagonal
Point n-1 has 0 diagonals
Point n has 0 diagonals

So an 11-sided figure would have 44 diagonals.

The general formula being n(n-3)/2.

If you try this general formula for something that you can easily draw and count the diagonals of, such as a square or a pentagon, you will see it holds true. (A square has 2 diagonals = 4(4-3)/2 = 4/2 = 2. A pentagon has 5 diagonals = 5(5-3)/2 = 10/2 = 5.)

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Answer 2

17

Answer 3

There are 17.

Answer 4

I think the formula is x(x-1)/2 but I'm not sure