Hexagons Explained! The Complete Guide to Hexagons — Mashup Math (2024)

Hexagons Explained! The Complete Guide to Hexagons — Mashup Math (1)



by Anthony Persico

Hexagons Explained! The Complete Guide to Hexagons — Mashup Math (2)

What is a Hexagon? - Definition, Facts, Examples, and More!

Welcome to this complete guide to hexagons, where you will learn everything you need to know about this beautiful six-sided polygon!

Hexagon Definition:

Hexagons Explained! The Complete Guide to Hexagons — Mashup Math (3)

In mathematics and geometry, a Hexagon is defined as a polygon (a closed two-dimensional shape with straight sides) with 6 sides.

Note that Hexagons have 6 sides and 6 angles.

There are two types of Hexagons: Regular Hexagons and Irregular Hexagons.

What is a Regular Hexagon?

A regular hexagon is defined as a 6-sided polygon that is both equilateral and equiangular—meaning that all of the sides have the same length and all of the angles have the same measure.

What is an Irregular Hexagon?

An irregular hexagon is defined as a 6-sided polygon that is not regular—meaning that all of the sides and angles do not have the same measure.

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What are the Properties of a Regular Hexagon?

In Geometry, you will most often be dealing with regular hexagons. It is important to know their three main properties:

  • All sides of a regular hexagon have equal lengths.

  • All of the interior angles of a regular hexagon are 120° each.

  • The total sum of the interior angles is 720°.

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What Is a 3D Hexagon?

In Geometry, a 3D Hexagon is called a Hexagonal Prism—which is a prism with hexagonal base.

In the case of 3D hexagons, the hexagonal base is usually a regular hexagon.

For example, a truncated octahedron can be considered a 3D Hexagon because it has a hexagonal base.

Here are a few more examples of 3D Hexagons:

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Convex Hexagons vs. Concave Hexagons

In Geometry, a polygon is can be convex or concave.

  • For a hexagon to be convex, all of its interior angles must be less than 180°.

  • For a hexagon to be concave, at least one of its interior angles must be greater than 180°.

For example, a regular hexagon is also a convex polygon because all of the interior angles equal 120°, which is less than 180°.

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Hexagons Degrees: Why 720°?

As previously stated, the measure of each interior angle in a hexagon is 120° and the total sum of all of the interior angles is 720°.

But why? Since there are 6 angles in a regular hexagon and each angle equals 120°, the total sum would be:

120 + 120 + 120 + 120 + 120 + 120 = 720

or

120 x 6 = 720

Furthermore, you can use the polygon interior sum formula to find the sum of the interior angles for any regular polygon.

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By applying the polygon interior sum formula to a hexagon, you replace n with 6 (since a hexagon has 6 sides) as follows:

(n - 2) x 180° ➞ (6 - 2) x 180° = 4 x 180° = 720°

Hexagons in Real Life

The hexagon is a simple yet remarkable shape that can be found everywhere and anywhere—ranging from art to architecture to nature. Here a few remarkable examples of hexagons in real life:

Hexagons in Real Life: Snowflakes

Did you know that all snowflakes are hexagons? When ice crystals form, the molecules join together in a hexagonal structure. Mother Nature has determined that this type of formation is the most efficient way for snowflakes to form.

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Hexagons in Real Life: Honeycombs

Regular hexagons are one of only three polygons that will tesselate a plane—meaning that they can be duplicated infinitely to fill a space without any gaps. And when bees build honeycombs, they choose to use hexagons. Always!

Hexagons in Real Life: Architecture

Bees are not the only ones who understand the power and efficiency of hexagons. Ancient and modern architecture constantly utilizes this shape from floor tiles to windows to ornate ceiling designs. Hexagons are everywhere!

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Hexagons in Real Life: Art

Due to their beautiful form and ability to tessellate, hexagons are constantly used in art and graphic design to create patterns, mosaics, logos, and more!

In fact, many companies choose a hexagon shape for a logo because it represents strength and security.

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Hexagons in Real Life: Religion

Since regular hexagons often show up in nature (like snowflakes and honeycombs) they are often included in Sacred Geometry, which assigns higher meaning and spirituality to certain shapes and proportions. In fact, some view the hexagon as the most fascinating shape in relation to the universe.

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Hexagons Explained! The Complete Guide to Hexagons — Mashup Math (2024)

FAQs

What are the four types of hexagons? ›

All hexagons have six sides, regardless of the type of hexagon it is. This means that regular hexagons, irregular hexagons, concave hexagons and convex hexagons all have six sides each.

Is a hexagon 6 or 8 sides? ›

In geometry, a hexagon can be defined as a closed two-dimensional polygon with six sides. Hexagon has 6 vertices and 6 angles also. Hexa means six and gonia means angles.

How do you solve a math hexagon? ›

To determine the area of a hexagon with perimeter P :
  1. Divide P by 6 to get the side length a .
  2. Find the square of the side length: a² .
  3. Multiply a² by 3√3 / 2 .
  4. The result is the area of your hexagon!
  5. You could also go directly from P to the area by using the formula area = √3 P² / 24 .

What is a 6 sided polygon in real life? ›

A regular hexagon shape has six sides that are equal in length, six interior angles that are equal in size and six exterior angles that are equal in size. Some examples of real life regular hexagons include floor tiles and honeycomb in beehives which form tessellating hexagonal patterns.

What is a 3D hexagon called? ›

A prism is a 3D shape with a constant polygon shaped cross-section. A prism is named by the shape of its polygon cross-section. When the cross-section is a triangle, the prism is called a triangular prism. When the cross-section is a hexagon, the prism is called a hexagonal prism.

What is a 7-sided shape called? ›

In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon.

Are hexagons stronger than triangles? ›

The list of structures from strongest to weakest are: (1) cylinder (averaging 164.8 kg of load at crushing weight), (2) hexagon (averaging 136.8 kg of load at crushing weight), (3) square (averaging 127 kg of load at crushing weight), (4) triangle (averaging 89.2 kg of load at crushing weight).

What is a hexagon shape in real life? ›

A honeycomb, a nut, white divisions of a volleyball, a stop board in traffic symbols, the back end of pencils and bolts are all examples of real-life objects that have the shape of a hexagon.

Do hexagons have corners? ›

One, two, three, four, five, six. A hexagon has six corners.

What is the math behind a hexagon? ›

In a regular hexagon, all sides are the same length, and each internal angle is 120 degrees. The area of a regular hexagon is commonly determined with the formula: area = 3√3/2× side2In an irregular hexagon, the sides are of unequal length, and each internal angle can be more or less than 120 degrees.

What polygon has 1000000000 sides? ›

A really, really big and precise circle, perhaps. Et voila! A megagon or 1 000 000-gon is a polygon with 1 million sides (mega-, from the Greek μέγας megas, meaning "great"). Even if drawn at the size of the Earth, a regular megagon would be very difficult to distinguish from a circle.

What shape has 12 sides? ›

A dodecagon is a polygon with 12 sides.

What is a polygon with 666 sides? ›

So the 666-sided polygon would be called a hexakosihexekontahexagon or hexakosihexakonahexagon (Attic Greek).

What is hexagon class 4? ›

A regular hexagon is a closed shape polygon which has six equal sides and six equal angles. In case of any regular polygon, all its sides and angles are equal.

What are the first four hexagonal numbers? ›

The first few hexagonal numbers (sequence A000384 in the OEIS) are: 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946... Every hexagonal number is a triangular number, but only every other triangular number (the 1st, 3rd, 5th, 7th, etc.) is a hexagonal number.

What is the classification of hexagon? ›

A hexagon is a two-dimensional flat shape that has six angles, six edges, and six vertices. It can have equal or unequal sides and interior angles. It is a 6-sided polygon classified into two main types - regular and irregular hexagon.

How many types of magic hexagon are there? ›

You see that, if there is a magic hexagon, it must have the order 3. It exists! It is amazing that there is only one magic hexagon. It isn't easy to find the distributions of the numbers 1 to 19.

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