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!

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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

How do you solve a math hexagon? ›

If the side length of a regular hexagon is 6 units, the area can be calculated with the formula, Area of hexagon = (3√3 s2)/2; where 's' is the side length. On substituting the value of s = 6 in the formula, Area of hexagon = (3√3 × 62)/2 = (3√3 × 36)/2 = 93.53 square units.

What is the math behind the hexagon? ›

The hexagon formula calculates the perimeter, area, and diagonals of the hexagon. The hexagon formulas apply directly to regular hexagons. The hexagon formulas are given as, Area of hexagon = (3√3s2)2 ( 3 3 s 2 ) 2 and Perimeter of hexagon = 6s, where s = side length.

What do all hexagons equal? ›

It has 6 equal sides and 6 equal angles. It has 6 vertices. Sum of interior angles equals 720°. Interior angle is 120° and exterior angle is 60°.

Is any 6-sided shape a hexagon? ›

How many sides does a hexagon have? 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.

What is a hexagon answer? ›

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.

What is the formula for a hexagonal number? ›

Hexagonal numbers: a(n) = n*(2*n-1). It is well known that for n>0, A014105(n) [0,3,10,21,...] is the first of 2n+1 consecutive integers such that the sum of the squares of the first n+1 such integers is equal to the sum of the squares of the last n; e.g., 10^2 + 11^2 + 12^2 = 13^2 + 14^2.

What is a 7-sided shape called? ›

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

What shape is 120 degrees? ›

Hexagon

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 the rule of a hexagon? ›

The sum of all interior angles is equal to 720 degrees, where each interior angle measures 120 degrees. The sum of all exterior angles is equal to 360 degrees, where each exterior angle measures 60 degrees.

What are 3 examples of hexagons? ›

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.

What's bigger than a hexagon? ›

Types of Polygon With Sides 3 to 20
Name of the PolygonsSidesVertices
Hexagon66
Heptagon77
Octagon88
Nonagon (also called Enneagon)99
15 more rows

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.

Are hexagons parallelograms? ›

Part of the definition of a Parallelogram is that it is a quadrilateral, so it must have exactly 4 sides. This detail is often overlooked and only the two pairs of parallel sides is emphasized. But every Hexagon has 6 sides, so a hexagon is never a Parallelogram.

Is a hexagon 180 or 360? ›

A hexagon can be divided into four triangles, therefore the sum of the interior angles of a hexagon is 180 × 4 = 720. The interior angles in a hexagon sum to 720°.

What is the formula for finding sides of a hexagon? ›

If you have a hexagon that's measured from one vertex (corner) across to the opposite vertex, you don't need to use a formula: just divide the width by 2, and that's your answer. For example, a hexagon that measures 10 cm from one vertex to the opposite vertex has sides of 5 cm.

What is the formula for the angle of a hexagon? ›

A hexagon has six sides, and we can use the formula degrees = (# of sides – 2) * 180. Then degrees = (6 – 2) * 180 = 720 degrees. Each angle is 720/6 = 120 degrees. Quantity B is greater.

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