# How many diagonals does a convex polygon have?

## How many diagonals does a convex polygon have?

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).

### How many diagonals can a convex 12 sided polygon have?

Soooooooo we can draw 54 diagonals in a 12 sided figure.

#### How many diagonals are in a 13 sided convex polygon?

A 13-gon would have 13(13-3)/2 = 65 diagonals.

**How many diagonals does an N sided convex polygon have?**

Let there be a polygon ( I am assuming a convex polygon) of n sides. but, as each diagonal has been counted twice, as it was counted as fresh diagonal when either of the vertices at its ends was considered, but actually we have only one diagonal.

**How many diagonals a convex Pentagon has?**

5 diagonals

The red line segments are all diagonals. This pentagon has 5 diagonals. Whether a polygon is convex or concave, it is always named by the number of sides. Explore the relationship between the number of sides of a convex polygon and its diagonals.

## How many diagonals are there in convex Pentagon?

5

Answer. To find the total number of diagonals in a polygon, multiply the number of diagonals per vertex (n – 3) by the number of vertices, n, and divide by 2 (otherwise each diagonal is counted twice)….Solved Examples.

Polygon Name | Number of Sides | Number of Diagonals |
---|---|---|

Pentagon | 5 | 5 |

Hexagon | 6 | 9 |

Heptagon | 7 | 14 |

### Are there in a polygon having 12 sides?

In geometry, a dodecagon or 12-gon is any twelve-sided polygon.

#### What’s a 13 sided shape called?

Tridecagon

A 13-sided polygon, sometimes also called the triskaidecagon.

**How many diagonals has a 20 sided convex polygon?**

170 diagonals

That is “3” less than the number of sides. Therefore, for a 20-sided polygon, there will be 190 lines and 170 diagonals.

**What is n sided convex polygon?**

All regular simple polygons (a simple polygon is one that does not intersect itself anywhere) are convex. Those having the same number of sides are also similar. An n-sided convex regular polygon is denoted by its Schläfli symbol {n}.

## How many diagonal are there in a polygon with n sides?

An n sided polygon has n vertices. If we join every distinct pair of vertices we will get nC2 lines. These nC2 lines include the n sides of the polygon as well as its diagonals. So the number of diagonals is given by the expression nC2 – n.

### How many diagonals are there in a convex polygon?

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

#### How to find the number of diagonals in an octagon?

A octagon has 20 diagonals. Define the formula. 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. [8]

**What does a diagonal mean in a polygon?**

A diagonal is any line segment drawn between vertices of a polygon that doesn’t include the sides of that polygon. A polygon is any shape that has more than three sides.

**How many sides does a polygon have in it?**

You may need to first identify how many sides are present in the polygon. Each polygon has a prefix that indicates the number of sides it has. Here are the names of polygons with up to twenty sides: Quadrilateral/tetragon: 4 sides; Pentagon: 5 sides; Hexagon: 6 sides; Heptagon: 7 sides; Octagon: 8 sides; Nonagon/Enneagon: 9 sides