Bunuel wrote:

How many diagonals does a regular 11-sided polygon contain?

A. 35

B. 38

C. 40

D. 44

E. 55

A nice/fast approach that doesn't involve any counting techniques is to recognize that, for each of the 11 points (vertices), there are 8 possible points that we can connect to to create a diagonal.

ASIDE: there are 8 possible points because we cannot create a diagonal by connecting 2 adjacent points.

So, there are 8 possible diagonals for each of the 11 points

These means that there are 88 possible diagonals in total (8x11=88).

However, we need to recognize that this method counts each diagonal twice. For example, it counts the diagonal AB and the diagonal BA as 2 separate diagonals.

So, to account for this duplication, we'll divide 88 by 2 to get 44

Answer:

Cheers,

Brent

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