# Heptagon like many diagonals

## Diagonals in regular polygons

This chapter is devoted to **Number and length of diagonals of regular polygons** as well as the arithmetic determination of the number of this diagonal.

### Number of diagonals:

Under one **diagonal **one understands in the plane geometry the **Connection route from non-adjacent corner points**.

Thus, depending on the number of corner points, polygons have **different numbers of diagonals**.

At a **triangle **there are only adjacent corner points, so this has a geometric surface **no diagonals**.

In one **square **2 opposite corner points can be connected to each other; thus has a square **two diagonals**.

Looking at a **pentagon**, you can see that the number of diagonals increases exponentially, because here you can already **five diagonals** are drawn.

In one **hexagon **can be **nine diagonals** draw in, etc.

### Length of the diagonals:

The diagonals of one **regular quadrilateral** and **regular pentagon** are each of the same length.

For **Polygons** with more than five corner points, this knowledge applies **Not**! Here the diagonals have different lengths.

### Calculate the number of diagonals:

The number of diagonals of a (regular) polygon with **tease** can be done with the help of the following **formula **determine arithmetically:

This results in the following number of diagonals for polygons:

tease | d diagonals |
---|---|

3 | 0 |

4 | 2 |

5 | 5 |

6 | 9 |

7 | 14 |

8 | 20 |

9 | 27 |

10 | 35 |

11 | 44 |

12 | 54 |

13 | 65 |

14 | 77 |

15 | 90 |

**Diagonals in regular polygons**

Under

**Diagonals**one understands in the plane geometry

**Connections from non-adjacent corner points**.

The

**Number of diagonals**of a (regular) polygon with

**tease**can be done with the help of the following

**formula**determine arithmetically:

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