How Many Diagonals are There in a Regular Hexagon

Introduction

A hexagon is a two-dimensional geometric shape with six sides that may or may not have the same length. The hexagon shape can be found in a variety of real-world objects, including floor tiles, pencils, clocks, honeycombs, etc. Either it is regular (has six equal sides and angles) or irregular (has six different side lengths and angles).

Regular Hexagon

A closed, two-dimensional shape with six equal sides and six equal angles is referred to as a regular hexagon. The regular hexagon has 120 degree angles on each side. And 120 x 6 = 720 degrees is the total of all interior angles. We are aware that any polygon's exterior angles add up to 360° when considering their totals. In a hexagon, there are 6 exterior angles. Thus, the exterior angles of a regular hexagon are each 360 / 6 = 60 degrees in length.

An irregular hexagon differs from a regular hexagon in that the lengths of the sides are different and the angles are not clearly defined. Here are a few characteristics that both regular and irregular hexagons share:

• Both have 6 vertices, 6 interior angles, and 6 sides.

• All six interior angles add up to 720 degrees.

• The total of all six exterior angles is always 360 degrees.

Diagonals of Hexagon

A diagonal is a section of a line that joins any two non-adjacent polygonal vertices. In a hexagon, there are essentially two types of diagonals: long diagonals (those with three diagonals that cross the centre) and short diagonals. The equation "2s" can be used to calculate the length of each long diagonal in a regular hexagon. And the formula "\sqrt{3}s ," where s is the length of each hexagonal side, can be used to calculate the length of each short diagonal.

Method of calculation

In order to answer this question, we will use the relationship between a polygon's number of sides and diagonals. The formula for an n-sided polygon's number of diagonals is D_{n}=\frac{n(n-3)}{2} .

Here given is a regular hexagon. Six equal sides and angles make up a regular hexagon, which is also a polygon. Thus, a regular hexagon has six sides.

Using the relationship between the number of sides and diagonals now, we have -

D_{n} = \frac{n(n-3)}{2} , where D_{n} = number of diagonals.

So, the regular hexagon value of n is 6.

\Rightarrow D_{n}= \frac{6(6-3)}{2}

\Rightarrow D_{n}= \frac{6\times 3}{2}

\Rightarrow D_{n}= \frac{18}{2}

\Rightarrow D_{n}= 9

.

Conclusion

Therefore, there are 9 diagonals in a regular hexagon.