# Properties Of Hexagon: Regular and Irregular with Solved Examples

Properties Of Hexagon: Six sides make up a hexagonal polygon. It’s possible that you’ve seen polygonal properties such as parallelograms, squares, and triangles. Each polygon has unique characteristics. Six sides and six angles make up a hexagon. For a regular hexagon, they are all equal; for an irregular hexagon, they are all unequal.

## What is Hexagon?

Six sides and six angles make up the shape known as a hexagon. Similar to an illustration on paper, it is a two-dimensional, flat shape. The cross-section of a pencil, a clock face, hexagon-shaped floor tiles, and honeycomb cells are a few real-world instances of hexagons.

Regular hexagons and irregular hexagons are the two different forms of hexagons. Every side and angle of a regular hexagon have the same length and measurement. This indicates that every internal angle and every side of a regular hexagon have the same measurements. Conversely, the sides and angles of an irregular hexagon vary in length and measurement.

## Types of Hexagon

Hexagons can be classified into 4 categories according to the length of their sides and angles. These categories are as follows:

Regular Hexagon: A regular hexagon is a hexagon with equal sides and angles. A regular hexagon’s interior and exterior angle sums are 720° and 360°, respectively.

Irregular Hexagon: An irregular hexagon possesses uneven sides and angles. An irregular hexagon’s interior angles still add up to 720°, but they don’t measure 120° each.

Convex Hexagon: A convex hexagon is one whose internal angles total less than 180°. The length of the sides and the angles determine whether it is regular or irregular.

Concave Hexagon: A concave hexagon is one that has at least one internal angle that is more than 180 degrees. It is consistently an asymmetric hexagon.

Also Read: 50+ Greatest Common Factor Questions

## Properties of Hexagon: Regular

The properties of a regular hexagon include:

Six sides: There are six sides of equal length in a regular hexagon.

Six angles: A typical hexagon has six angles, each measuring 120 degrees. A regular hexagon has congruent angles all around.

Equal side lengths: A regular hexagon has equal lengths on all of its sides.

Equal angles: A regular hexagon has congruent angles, each measuring 120 degrees.

Nine diagonals: There are nine line segments that connect non-adjacent vertices in a regular hexagon.

Sum of inner angles: A typical hexagon’s interior angles add up to 720 degrees. The formula (180degrees×(n−2)), where n is the number of sides, can be utilised to calculate this.

Sum of exterior angles: A normal hexagon’s external angles add up to 360 degrees. Regular hexagons have 60 degrees for each of their external angles.

Axes of symmetry: Six axes of symmetry go across a regular hexagon. Of these axes, three cross diagonals that are opposite to the vertices, while the other three cross the midpoints of edges that are opposite to each other.

Equilateral triangles: Six congruent equilateral triangles can be formed from a regular hexagon. By joining the hexagon’s centre to each vertex, a triangle is created.

Circumcircle: A regular hexagon can be encircled by a circle that goes through each of its six vertices. The circumcircle’s radius is the length of time from its centre to any vertex, and its centre is the same as the hexagon’s centre.

## Properties of Hexagon: Irregular

The properties of an irregular hexagon include:

Uneven side lengths: An irregular hexagon has uneven side lengths.

Unequal angles: An irregular hexagon’s interior angles may vary in size.

Diagonals: Depending on how its sides and vertices are arranged, an irregular hexagon may have a different number of diagonals.

Sum of inner angles: An irregular hexagon’s internal angles add up to 720 degrees, in accordance with the general polygon property.

Sum of exterior angles: An irregular hexagon’s exterior angles always add up to 360 degrees, in accordance with the general polygon property.

No axes of symmetry: Because the angles and sides of an irregular hexagon are not organised symmetrically, they lack axes of symmetry.

## Properties of Hexagon: Solved Examples

1.  Find the measure of interior angle if a regular polygon has 10 sides.

Solution,

For a regular polygon of “n” sides, the measure of interior angle is:

180 – {360/n}

For n = 10,

Interior angle = 180 – {360/10} = 144°

1. If the interior angle of a regular polygon is 80°, what regular polygon will we get? (3 marks)

Solution,

Interior angle = 180 – {360/n}

80° = 180 – {360/n}

360/n = 180° – 80°

360/n = 100°

n = 3.6

1. The perimeter of a regular hexagon is 36 cm. What is the length of its sides?

Solution,

Perimeter of regular hexagon = 6 × length of side

36 = 6 × length of side

Length of side = 366 cm = 6 cm

So, the length of its sides is 6 cm

## FAQs

What properties does a hexagon have?

The following are a hexagon’s primary characteristics: A polygon with six sides and six vertices is called a hexagon. A hexagon’s interior angles always add up to 720 degrees always. One side’s length can be multiplied by six to find a hexagon’s perimeter. There are nine diagonals in a hexagon; they are line segments that join vertices that are not adjacent.

What do a hexagon’s diagonals mean?

Line segments that join a hexagon’s non-adjacent vertices, or corners, are called diagonals. There are nine diagonals in a hexagon.

Are all shapes with six sides are hexagons?

Yes, hexagons are the name given to all six-sided shapes.

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