Question

QUESTION
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Derive the formula for finding the number of diagonals in polygon.







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Harsh Pratap Singh ​

Answer 1

$\huge\underline\red{ANSWER}$

We can simply derive using the following meathod:-

For each vertex n(vertices) you have (n−3) possible vertices to create a diagonal from.

Why (n−3)? Because you can't combine with the 2 neighboring vertices and you can't combine with your current vertex. Divide by two because you are counting twice. So you have (n−3)n/2 diagonals.

Answer 2

Answer:

The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides. For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3).