Have you ever wondered what a six sided figure is called? Perhaps you’ve encountered a shape with six sides in your everyday life, but you’re unsure of what to call it. Well, wonder no more! The technical name for a six sided figure is a hexagon. That’s right – it’s not just a fancy word to impress your friends. Hexagons are all around us, from the honeycomb pattern in beehives to the markings on a football field.
But what makes hexagons so special? Why do we see them so often in nature and manmade structures? The answer lies in their unique geometry. Unlike squares or rectangles, which have right angles and sharp corners, hexagons have angles that are 120 degrees. This allows them to fit together seamlessly, creating a strong and sturdy structure. That’s why we see hexagons used in everything from architectural designs to aerospace engineering.
Overall, hexagons are a fascinating shape with a rich history and practical applications. Whether you’re a math enthusiast or just a curious individual, understanding what a six sided figure is called is sure to come in handy. So why not take a closer look at the hexagons around you and appreciate the beauty and functionality of this unique shape?
Properties of Six-Sided Figures
A six-sided figure is a polygon with six angles and six sides. This type of polygon is also called a hexagon. Hexagons are fascinating shapes with unique properties that make them useful in various fields such as geometry, architecture, and engineering. In this article, we will explore the properties of six-sided figures and their practical applications.
- A hexagon has six sides that are all equal in length. This property makes the hexagon a regular polygon, meaning it has equal angles and sides.
- The sum of the internal angles of a hexagon is 720 degrees, or twice the sum of the angles of a triangle. Each angle of a regular hexagon is 120 degrees.
- A hexagon can be divided into six equilateral triangles by drawing lines connecting each vertex to the center of the polygon. This property helps in calculating the area of the hexagon by using the formula: A = 3√3s²/2 where A is the area and s is the length of a side.
Hexagons have a range of practical applications, including:
- Structural strength: Hexagonal structures are incredibly sturdy and can bear heavy loads. They are used in the design of bridges, buildings, and even spacecraft.
- Honeycomb: Honeycomb structures are made up of hexagons and are used in the manufacturing of composites for aerospace, marine, and automotive industries. The hexagonal shape ensures optimal strength, stiffness, and weight reduction.
- Tiling: Hexagonal tiles are used in interior and exterior designs due to their unique visual appeal and ability to create complex patterns.
Table: The internal angles of a hexagon
| Number of sides | Sum of interior angles |
|---|---|
| 6 | 720° |
In conclusion, the hexagon is a six-sided figure with unique properties that make it useful in many fields. Its equal sides and angles, coupled with its ability to divide into equilateral triangles, make it an essential shape in geometry. Our understanding of the hexagon’s strength, stiffness, and aesthetic appeal continues to expand as we explore its practical applications in architecture, engineering, and manufacturing.
Classification of Six-Sided Figures in Geometry
Geometry is the branch of mathematics that deals with the study of shapes, sizes, and positions of figures. Six-sided figures, also called hexagons, are classified in geometry based on their angles, sides, and properties. Understanding the different types of hexagons can help in solving geometry problems and identifying different shapes in the real world.
Types of Hexagons
- Regular Hexagon: A hexagon with all sides and angles equal is called a regular hexagon.
- Irregular Hexagon: A hexagon with sides and angles of different lengths and measures is called an irregular hexagon.
- Convex Hexagon: A hexagon with all its interior angles less than 180 degrees is called a convex hexagon.
- Concave Hexagon: A hexagon with at least one interior angle greater than 180 degrees is called a concave hexagon.
The regular hexagon, with all its sides and angles congruent, is the most symmetrical hexagon. A regular hexagon also has six lines of symmetry. On the other hand, the irregular hexagon has sides and angles of different measures, making it asymmetrical. A convex hexagon has all its interior angles less than 180 degrees and has no corners pointing inwards. A concave hexagon, on the other hand, has at least one interior angle greater than 180 degrees with corners pointing inwards.
Properties of Hexagons
Hexagons have different properties that help in their classification and identification. Some of the properties include:
- Perimeter: The perimeter of a hexagon is the sum of all its sides.
- Area: The area of a hexagon is the amount of space it occupies. The formula for the area of a regular hexagon is 3√3/2 x s^2, where s is the length of the side.
- Diagonal: The diagonal of a hexagon is a line segment connecting two non-adjacent vertices.
- Angle measure: The measure of each interior angle of a regular hexagon is 120 degrees, while that of an irregular hexagon varies depending on the lengths of its sides and angles.
The properties of a hexagon can be used to solve different geometry problems. For example, the area formula for a regular hexagon can be used to find the area of a beehive, which is made up of hexagonal cells. The diagonal of a hexagon can also be used to determine the distance between two opposite corners of a hexagonal tile floor.
Real-world Examples
Hexagons can be found in many natural and man-made objects. Some real-world examples include:
| Object | Use of Hexagon |
|---|---|
| Honeycomb | Built by bees for storing honey |
| Hexagonal tiles | Used for flooring, wall covering, and decorative designs |
| Snowflakes | Natural phenomenon with hexagonal symmetry |
Understanding the classification and properties of hexagons is essential in solving geometry problems and identifying different hexagonal shapes in the real world. Whether it’s in natural formations, such as snowflakes, or man-made objects, like hexagonal tiles, hexagons are a crucial part of our world.
Identifying Regular vs Irregular Hexagons
A hexagon is a six-sided polygon. The word “hexagon” comes from the Greek words “hexa” meaning six and “gonia” meaning corner. There are two types of hexagons: regular and irregular. The difference between the two lies in their shape and sides.
- Regular Hexagons: A regular hexagon is a shape with six equal sides and angles. All of the sides are the same length, and all of the angles measure 120 degrees. Regular hexagons look like a perfect geometric shape, and each of its sides is congruent to and parallel to the opposite side.
- Irregular Hexagons: An irregular hexagon is a shape with six sides that are not equal or angles that are not of equal degrees. Simply put, its sides can have different lengths and angles. Irregular hexagons can look like random shapes or have similar shapes to other polygons with more or less than six sides.
Regular hexagons are commonly found in nature, such as honeycombs, basalt columns, and snowflakes. Irregular hexagons, on the other hand, can be found in many different shapes, such as stop signs, traffic cones, and irregularly shaped tiles.
Properties of Regular Hexagons
Regular hexagons have specific properties that set them apart from irregular hexagons. These include:
| Property | Regular Hexagons |
|---|---|
| Sides | All sides are congruent. |
| Angles | All angles measure 120 degrees. |
| Perimeter | The perimeter of a regular hexagon is equal to the sum of its six sides. |
| Area | The formula for the area of a regular hexagon is A = (3√3 / 2) x s^2, where s is the length of one of its sides. |
| Circumcircle | A regular hexagon can be inscribed in a circle with a radius equal to the length of its side. The center of that circle is also the center of the hexagon. |
Knowing the properties of regular and irregular hexagons can help in solving geometric problems. A regular hexagon is a useful shape in engineering, design, and architecture, as it provides a strong, stable, and symmetrical foundation for building structures. Understanding the difference between regular and irregular hexagons can also help in differentiating between shapes and identifying patterns in nature and art.
Real-life examples of objects with hexagonal shapes
A six sided figure with six angles and six vertices is called a hexagon. It is one of the most fascinating geometric shapes, and there are many real-life examples of objects with hexagonal shapes. These hexagonal objects can be found in nature or in man-made structures, and their uses are vast.
- Honeycomb: Honeycomb is a perfect example of hexagonal shapes in nature. It is a structure made by bees to store honey and to raise their young ones. The hexagonal shape of honeycomb allows bees to maximize storage space while using the least amount of the wax.
- Bolts and screws: Hexagon headed bolts and screws are widely used in construction and manufacturing. The hexagonal shape makes the bolts and nuts easy to grip and turn without slipping while tightening or loosening.
- Nanotubes: Nanotubes are tiny tubes made of hexagonal shapes and have a diameter of a few nanometers. These tubes have many potential uses in the fields of medicine, electronics, and energy storage technology.
Benefits of hexagonal shapes
The hexagonal shape has several benefits. It is a stable and sturdy shape, making it useful in construction to create structures that can withstand high pressure or weight. Hexagonal structures also have a higher strength-to-weight ratio, making them useful in objects that need to be lightweight, like aircraft or car components.
Hexagonal shapes also have aesthetic qualities, and they are often used in art and design to create visually appealing patterns and textures. Furthermore, hexagons are symmetrical and have an equal angle at each corner, making them perfect for tiling floors, walls, and ceilings.
Hexagonal shapes in architecture
Hexagonal shapes have been used in architecture for centuries. The most famous example is the hexagonal dome of the Florence Cathedral in Italy. The hexagonal shape of the dome allowed for a greater distribution of weight, enabling the construction of a much larger, more impressive dome than was previously possible.
| Building | Location | Year Built |
|---|---|---|
| Beijing National Stadium | Beijing, China | 2008 |
| Fleur-de-Lis Museum | Madrid, Spain | 2010 |
| City of Arts and Sciences | Valencia, Spain | 1996-2009 |
The Beijing National Stadium, also known as the Bird’s Nest, is another example of hexagonal shapes in architecture. The stadium was built for the 2008 Olympics and has become one of the most iconic buildings in China. The structure of the stadium is formed by a series of interlocking steel beams, which create a unique hexagonal pattern.
Hexagons in Nature and Biology
Hexagons, with their six equal sides and angles, are a common shape found in nature and biology. From honeycombs to turtle shells, here are some examples of hexagons in the natural world:
- Honeycombs: Bees are well-known for their ability to construct hexagonal honeycomb cells. The shape allows for maximum storage space while minimizing the amount of wax and energy used in construction.
- Turtle shells: A turtle’s shell is made up of hexagonal plates called scutes. These plates interlock and overlap for added protection and flexibility.
- Snowflakes: While not all snowflakes are hexagonal, many do exhibit six-fold symmetry due to the way water molecules attach to each other as they freeze.
Hexagons in Biological Systems
Beyond their appearance in natural structures, hexagons also play a role in biological systems. For example:
The hexagonal lattice is a common structure in protein crystals, due to the optimal packing efficiency it allows. In fact, hexagonal packing is the most efficient way to pack circular objects, which is why it’s a popular shape for fruits and vegetables like oranges and pineapple.
| Organism | Structure |
|---|---|
| Carbon | Hexagonal graphene sheets |
| Cells | Hexagonal cell packing in epithelial tissues |
| Hemoglobin | Hexagonal arrangement in red blood cells |
As you can see, hexagons are both a visually striking and functionally efficient shape that appears repeatedly in nature and biological systems.
History and Cultural Significance of Hexagons
The number 6 holds a special place in many cultures and religions. It is considered a perfect number in mathematics, as it is both the sum and the product of its factors: 1, 2, and 3. In geometry, a six-sided polygon is called a hexagon. The hexagon has been used in architecture, art, and symbolism throughout history.
The earliest known use of hexagons was in the construction of beehives by the ancient Greeks. The hexagonal shape allowed for the most efficient use of space, and the bees could easily move around the hive. The hexagon’s efficiency in terms of space proves to be beneficial not only in the hives but also in many industrial applications like the shape of bolts and nuts.
In Hinduism, the hexagon is known as the Sri Yantra. It is a symbol of balance, harmony, and prosperity. The hexagon is also used in Islamic architecture, where it represents the seven stages of heaven. In Judaism, the Star of David is a hexagram, which symbolizes the connection between God and the Jewish people.
Cultural Examples of Hexagons
- The famous structure of Giant’s Causeway in Northern Ireland is a natural formation of hexagonal rock columns, making it an iconic symbol and a UNESCO World Heritage Site.
- The Japanese art form of origami often includes a six-sided shape called a hexagon twist.
- The soccer ball has 20 hexagonal and 12 pentagonal panels, creating a spherical shape.
Hexagonal Patterns in Art
The hexagon has been widely used in art and design. The symmetry and repeating pattern of hexagons create a visually pleasing effect. The art style known as tessellation, which uses repeating shapes to create a pattern, often uses hexagons. The hexagon has been used in tile designs, mosaics, and stained glass windows.
One of the most famous examples of hexagonal patterns in art is the honeycomb pattern. The hexagonal cells in the honeycomb are not only practical for the storage of food and brood but also aesthetically pleasing. This pattern is often used in textile design, wallpaper, and furniture fabrication.
| Artist | Artwork |
|---|---|
| MC Escher | Metamorphosis III |
| Albrecht Dürer | Melencolia I |
| Victor Vasarely | Zebra |
The hexagon’s use in art and design throughout history illustrates its importance and versatility in various cultural contexts.
The use of hexagons in art and design
Hexagons are six-sided figures that have been used in various art and design forms for centuries. They are known for their unique, geometric shape that allows for endless creative possibilities. The repetition of hexagons in a design can create a beautiful sense of symmetry and balance.
The beauty of the number seven in hexagon design
- The number seven is often used in hexagon design due to its significant meaning in many cultures and religions.
- There are seven days in a week, seven wonders of the world, and seven colors in a rainbow.
- In Islamic art, the seven-pointed star is a common design element and is thought to represent the seven heavens.
Hexagons in modern graphic design
Today, hexagons are commonly used in modern graphic design for packaging, logos, and branding. The hexagon’s shape can convey a sense of stability, harmony, and unity. Some common uses of hexagons in modern graphic design include:
- Honeycomb designs for products such as soap, candles, and perfume.
- Hexagonal shapes for logos, such as the popular design for the video game company, Ubisoft.
- Geometric patterns using hexagons for packaging and branding, as seen in the design for Australian beer company, Stone & Wood.
Examples of hexagon art and design throughout history
Hexagons have been used in art and design for centuries, from ancient mosaics to modern architecture. Here are a few notable examples:
| Art/Design | Description | Time Period |
|---|---|---|
| Alhambra Palace | The intricate geometric patterns in the palace’s tiles feature hexagons and other shapes. | 14th century |
| Honeycomb Cell | Inspired by honeycomb, a newly discovered structure, Robert Hooke illustrated this view of cork. | 1665 |
| Crystal structure of snowflakes | Snowflakes have hexagonal symmetry due to the way water molecules bond together. This structure was first observed by Wilson ‘Snowflake’ Bentley. | Early 1900s |
From ancient Islamic art to modern graphic design, hexagons have proven to be a timeless and versatile geometric shape that continues to inspire art and design today.
What is a six sided figure called?
Q: What is a six sided figure called?
A: A six sided figure is called a hexagon.
Q: What does “hexagon” mean?
A: “Hexagon” comes from the Greek words “hex” (six) and “gonia” (angles).
Q: What are some examples of hexagons in nature?
A: Honeycomb cells, snowflakes, and turtle shells are all examples of hexagons in nature.
Q: What are some real-life uses of hexagons?
A: Hexagons are used in construction, such as in the shape of tiles and bricks. They are also used in honeycomb structures for aerospace engineering and in the design of heat exchangers.
Q: What is the difference between a regular hexagon and an irregular hexagon?
A: A regular hexagon has six equal sides and six equal angles, while an irregular hexagon has sides and angles of different measurements.
Q: What is the formula for calculating the area of a hexagon?
A: The formula for calculating the area of a regular hexagon is (3√3)/2 multiplied by the square of the length of one side.
Q: How can I draw a hexagon?
A: One way to draw a hexagon is to use a compass to draw a circle. Then, place the compass on the edge of the circle, and mark off six points at equal intervals. Connect these points with straight lines to form a hexagon.
Closing Thoughts
Thanks for reading! Hexagons are interesting shapes with many real-life applications. From construction to aerospace engineering, hexagons are everywhere. Next time you come across a hexagon, take a closer look and appreciate its unique beauty. Visit again later for more interesting articles on various topics!