There are 9 diagonal in a hexagon. to calculate diagonal , apply formula = n(n-3)/2

Diagonals in a Hexagon

A hexagon is a polygon with six sides. Diagonals are line segments that connect non-adjacent vertices in a polygon. In the case of a hexagon, diagonals are line segments that connect any two non-adjacent vertices within the shape. To determine the number of diagonals in a hexagon, we need to consider a few key points.

Understanding Diagonals

Diagonals are formed by connecting two vertices that are not adjacent, creating line segments within the polygon. In a hexagon, each vertex is connected to four other vertices, resulting in six possible diagonals for each vertex. However, we must take into account that each diagonal is counted twice since it connects two vertices.

Calculating the Number of Diagonals

To calculate the number of diagonals in a hexagon, we can use the following formula:

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

where n represents the number of sides of the polygon. In this case, n is equal to 6 since a hexagon has six sides.

Using the formula, we can substitute the value of n into the equation:

Number of diagonals = (6 * (6 - 3)) / 2
Number of diagonals = (6 * 3) / 2
Number of diagonals = 18 / 2
Number of diagonals = 9

Therefore, a hexagon has 9 diagonals.

Visualization

To better understand the concept, let's visualize a hexagon:

```
A-------B
/ \
/ \
F C
| |
| |
E D
\ /
\ /
F-------E
```

In this hexagon, the diagonals can be observed connecting the non-adjacent vertices:

- Diagonals: AD, AE, AF, BD, BE, BF, CD, CE, and CF (9 diagonals in total)

Conclusion

In summary, a hexagon has 9 diagonals. Diagonals are line segments that connect non-adjacent vertices within a polygon. By using the formula (n * (n - 3)) / 2, we can calculate the number of diagonals in any polygon, including a hexagon.