how many diagonals does a 12 sided polygon have?

Question

What is a in and out chart?

Answer 1

Think of each vertex (12) of them. Each vertex can connect to 9 other vertices (not counting itself and the 2 adjacent vertices).

So that is 12 x 9. But that double counts them. So divide by 2.

12 x 9 / 2 = 54 diagonals.

In general, for an n-sided polygon, there are n(n-3) / 2 diagonals.

Several people are getting the wrong answer when they say it is C(12, 2). In doing that, you are counting the edges of the polygon.

Notice how if you take 66 - 12 you get 54 diagonals, so another generalized formula for the number of diagonals is C(n, 2) - n.

Expanded out that would be
n! / (n-2)! 2! - n.

That simplifies to
n (n-1) / 2 - n.

Finding a common denominator of 2:
[ n (n-1) - 2n ] / 2

Pulling out the common n in the numerator:
[ n ( n -1 - 2 ) ] / 2

Finally simplifying the numerator:
n ( n - 3 ) / 2

So once again you get the same formula mentioned above. For n = 12, the number of diagonals is:
12 x 9 / 2 = 108 / 2 = 54

So the number of *diagonals* is 54.

Answer 2

12 Sided Regular Polygon

Answer 3

4 sided has 2 6 sided has 3 so a 12 sided has 6

Answer 4

Since we can choose any two vertices to form a diagonal except ones that are adjacent, the answer is 12C2-12. that is 66-12=54.

Answer 5

There's another question further down about a 26-sided polygon. Read that answer for everything you need to know.

As for this question, it's not 66.

Answer 6

66

Answer 7

12C2 = (12!)/(2!(12 - 2)!)
12C2 = (12!)/(2! * 10!)
12C2 = (12!)/(2 * 10!)
12C2 = 66 diagonals

Answer 8

12C2 -12=(12x11/2)-12=66-12=54