SOLUTION: Find the total number of diagonals for a polygon of n sides for the following values of n. (a) n = 7

Algebra ->  Angles -> SOLUTION: Find the total number of diagonals for a polygon of n sides for the following values of n. (a) n = 7      Log On


   

Question 1192034: Find the total number of diagonals for a polygon of n sides for the following values of n.
(a)
n = 7
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Consider a polygon with n sides.
This means we have n vertices.

Each of the n vertices connects to n-3 diagonals
The -3 is to exclude the two surrounding neighbors (which don't form diagonals but rather exterior sides), and the vertex itself.

There are n(n-3)/2 total diagonals.
The dividing by 2 aspect is to avoid double-counting
Eg: diagonal AC is the same as diagonal CA.

Plug in n = 7 to find that,
n(n-3)/2 = 7*(7-3)/2 = 7*4/2 = 28/2 = 14

Answer: 14 diagonals in a heptagon.