**Table Of Contents**

**Hexagon**

The hexagon form, a closed 2D figure made up of six straight lines, will be discussed on this page. Since a hexagon has six sides, six vertices, and six internal angles, it is a six-sided polygon. We shall examine hexagons’ attributes, including their internal angles, features, and diagonals.

The flat geometric shape of a hexagon has six sides and six angles. Hexagons can be found in a variety of everyday objects, such as floor tiles, pencil cross sections, clocks, honeycombs, and more. A hexagon can be regular, with six equal sides and interior angles, or it can be irregular, with six sides of varied lengths and six interior angles of various sizes.

**Hexagon Definition**

A hexagon is a polygon with six sides, according to the definition, and gets its name from the Greek words “hex” for six and “gonia” for corners. As a result, a hexagon has six exterior angles, six interior angles, and six sides.

**Regular Hexagon**

A regular hexagon is a closed, two-dimensional shape with six equal-length sides and six equal-sized angles. A regular hexagon’s inner angles are individually measured at 120 degrees, and the total of all six interior angles is 720 degrees (120 6 = 720). Additionally, the sum of the exterior angles of every polygon is always 360°, and a regular hexagon has six outside angles, each of which is 60° in length.

**Irregular Hexagon**

A polygon with six sides of differing lengths and six interior angles of various sizes is called an irregular hexagon. However, both regular and irregular hexagons have a number of characteristics, such as:

with six sides, six internal angles, and six vertices are both regular and irregular.

In both forms of hexagons, the total of the six inside angles is always 720°.

In both kinds of hexagons, the total of the six outer angles is 360°.

**Angles of Hexagon**

Six interior and six exterior angles make up a hexagon. While the sum of its outside angles is 360°, the sum of its six inside angles is 720°. The following are some characteristics of hexagonal angles:

**Regular Hexagon Angles**

A regular hexagon has an interior angle of 120°, which can be computed as 720° 6 = 120°.

A normal hexagon has six outside angles, each measuring 60 degrees, or 360 degrees multiplied by six equals 60 degrees.

**An irregular hexagon’s angles**

At least two of the angles of an irregular hexagon have different sizes.

**Hexagon Sides**

As shown in the accompanying illustration, a hexagon is a closed object with six straight edges. All six sides of a regular hexagon are the same length, whereas two sides of an irregular hexagon have different lengths. The circumference of the hexagon is equal to the total of its six sides.

By dividing the regular hexagon’s circumference by six, we may determine the length of each side if we know it. For instance, if a regular hexagon has a perimeter of 72 units, its sides will each be 72 6 = 12 units long.

**Diagonals of a Hexagon**

A diagonal is a line segment that joins two polygonal vertices that are not contiguous to one another. The formula n(n-3)/2, where ‘n’ stands for the number of sides of the polygon, can be used to calculate the number of diagonals in a polygon. The number of diagonals for a hexagon with six sides can be computed as 6(6 – 3) / 2 = 6(3)/2, which equals 9 diagonals.

Three of a hexagon’s nine diagonals cross across the middle of the shape.

**Types of Hexagon**

The lengths of the sides and internal angles of hexagons can be used to classify them. Based on these** **Thus, the following types of hexagons exist:

**Regular Hexagon:** This kind of hexagon has internal angles and equal-length sides. The external angles of a regular hexagon measure 60°, while each of its inside angles

measures 120°. A regular hexagon’s interior angles add up to 720°, or six times 120°. There are six times 60 degrees total in the outer angles, or 360°.

**Irregular Hexagon:** Hexagons that are irregular in shape have sides and internal angles that are all different sizes. Although the internal angles are not all exactly 120 degrees, their total is the same, or 720 degrees.

**Convex Hexagon:** A convex hexagon is a six-sided polygon with interior angles that measure less than 180°. It can have either equal or unequal side lengths and angles, making it either regular or irregular. In a convex hexagon, all the vertices point outwards.

**Concave Hexagon:** On the other hand, a concave hexagon is a hexagon with at least one interior angle measuring greater than 180°. At least one vertex points inwards in a concave hexagon.

**Properties Of Hexagon**

A hexagon is a flat, six-sided, two-dimensional form that can have equal or unequal sides and angles on each of its six flat sides. Some of a hexagon’s essential characteristics include:

- There are six vertices, six edges, and six sides to it.
- Both equal and uneven side lengths are possible.

- All internal angles in a regular hexagon are equal to 120°.
- Any hexagon’s interior angles add up to 720° in total.
- All of the exterior angles of a regular hexagon are equal to 60 degrees.
- Any hexagon’s outside angles add up to 360° in total.
- Nine diagonals make up a hexagon.
- Since all of a regular hexagon’s internal angles are smaller than 180°, it is a convex hexagon.

**Solved Example**

**Question 1**

**Find the area and perimeter of a hexagon, if all its sides have a length equal to 8cm.**

**Solution: **From the area and perimeter formula of a regular hexagon, we know;

Area = 3.0792 a^2 = 3.0792 × 8^2 = 197.92 cm^2

Perimeter = 6a = 6 × 8 = 48 cm

**Question 2**

** Determine the side length of a regular hexagon whose perimeter is 72 cm.**

**Solution: **72 cm is the perimeter given.

The formula tells us; Radius = 6 a

Therefore,

72 = 6a

Ora = 72/6 = 12cm

As a result, the side length of the supplied hexagon is 12 cm.