## Diagonal of polygon formula of a cube

A polygon’s diagonal is a piece of a line that links any two vertices that are not next to one another.

The nature of the polygon and the number of its sides determine the number of diagonals that are present as well as the characteristics of those diagonals. Before we go on to studying the formula for the diagonal of a polygon, let’s first go through what a polygon and what a diagonal is.

A polygon is a closed shape created by joining three or more individual line segments. A polygon’s diagonal is a line segment generated by connecting any two vertices that are not adjacent to one another. Let’s have a look at the formula for calculating the diagonal of a polygon, as well as some instances of issues that have already been addressed. You can rapidly determine how many potential diagonals a simple polygon with a few sides has by counting them all. When polygons have more sophisticated patterns, it might be challenging to count them all.

## The formula of Diagonal of polygon

To our good fortune, there is a simple formula that can be used to determine the number of diagonals included inside a polygon. Due to the fact that each vertex (corner) is linked to two other vertices through sides, the connections between the vertices cannot be termed diagonals. This vertex, like the previous one, is unable to link with itself in any way. As a direct consequence of this, we are going to cut by three the total number of possible diagonals right now.

This vertex, like the previous one, is unable to link with itself in any way. For instance, if you exclude the movement from the top hinge to the bottom opposite and back, our door only has two diagonals. Any potential solution will need half of the problem.

## Calculation Method for the Total Number of Diagonals

According to what was covered before, the number of diagonals emanating from a single vertex is the total no. of vertices minus 3 or sides, or (n-3).

Given that there are a total of N vertices, we may calculate that there are n(n-3) diagonals.

However, because each diagonal of the polygon has two ends, this would count each one of the diagonals twice. In order to arrive at the final formula, we need to do the last step of dividing by 2:

Number of distinct diagonals =n(n-3)/2

where,

n is the no. of sides.

### SOLVED EXAMPLES-

**Example 1:** Using the formula for the diagonal of a polygon, determine the number of diagonals of a decagon.

**Solution:**

n = 10 number of sides.

Calculating the number of diagonals-

n(n−3)/2

=10(10−3)/2

=10(7)/2=70/2=35

The number of diagonals in a decagon equals 35.