# How many diagonals will be there in an N-sided regular polygon?

## How many diagonals will be there in an N-sided regular polygon?

Number of Diagonals = n(n-3)/2 In other words, an n-sided polygon has n-vertices which can be joined with each other in nC2 ways. Now by subtracting n with nC2 ways, the formula obtained is n(n-3)/2. For example, in a hexagon, the total sides are 6. So, the total diagonals will be 6(6-3)/2 = 9.

## How do you find the number of distinct diagonals in a polygon?

The formula to find the number of diagonals of a polygon is n(n-3)/2 where “n” equals the number of sides of the polygon.

How many sides does a polygon have if it has 9 diagonals?

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diagonals, as each vertex has diagonals to all other vertices except itself and the two adjacent vertices, or n − 3 diagonals, and each diagonal is shared by two vertices….Polygons.

Sides Diagonals
7 14
8 20
9 27
10 35

What is the number of diagonals in a polygon of 12 sides and 20 sides?

There are 54 diagonals in a dodecagon. These diagonals can be calculated with the help of the formula: 1/2 × n × (n-3), where n = number of sides.

### What is an n-sided polygon?

An n-gon is a polygon with n sides; for example, a triangle is a 3-gon. A simple polygon is one which does not intersect itself. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.

### How many diagonals are there in a polygon with N sides permutations and combinations?

Out of these lines, n lines are the sides of the polygon. ∴ Number of diagonals of the polygon =n(n-1)2-n.

What are distinct diagonals?

The above formula gives us the number of distinct diagonals – that is, the number of actual line segments. It is easy to miscount the diagonals of a polygon when doing it by eye. Some people see them making three triangles, for 6 diagonals.

How do you find the sides of a polygon when given the diagonals?

By using the formula for the number of diagonals of a polygon with n sides, you can determine how many sides a polygon has if you know the number of diagonals it has. For example, if a polygon has 54 diagonals, find how many sides it has. Then, solve for n using algebra. First multiply both sides by 2.

#### How many diagonals are in a 7 sided polygon?

14
Classifying Polygons

Polygon Name Number of Sides Number of Diagonals
Pentagon 5 5
Hexagon 6 9
Heptagon 7 14

#### How many sides does a polygon have if it has 27 diagonals?

The polygon has 9 sides.

What is the number of diagonals in a polygon of 8 sides?

an octagon has 8(8−3)/2 = 8×5/2 = 20 diagonals.

How do you find the total diagonals of an n-sided polygon?

In other words, an n-sided polygon has n-vertices which can be joined with each other in nC2 ways. Now by subtracting n with nC2 ways, the formula obtained is n (n-3)/2. For example, in a hexagon, the total sides are 6. So, the total diagonals will be 6 (6-3)/2 = 9.

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## How many diagonals are there in n*(n-3)/2?

Since for an n-sided convex polygon, from each vertex, we can draw n-3 diagonals leaving two adjacent vertices and itself. Following this way for n-vertices, there will be n* (n-3) diagonals but then we will be calculating each diagonal twice so total number of diagonals become n* (n-3)/2

## Are the sides of a polygon always straight lines?

It should be noted the sides of a polygon are always a straight line. In a polygon, the diagonal is the line segment that joins two non-adjacent vertices. An interesting fact about the diagonals of a polygon is that in concave polygons, at least one diagonal is actually outside the polygon.

Why is it difficult to count the diagonals of a graph?

Past the heptagon, it gets more difficult to count the diagonals because there are so many of them. Beware of counting a diagonal more than once. Each vertex may have multiple diagonals, but that doesn’t mean that the number of diagonals is equal to the number of vertices times the number of diagonals.