Hexagons are 2D geometric polygons known for being in honeycombs and pencils. A hexagon has six sides and six interior angles.
What is a regular hexagon shape?
A regular hexagon is a 2D geometric polygon with six sides equal in length and six angles that are equal in size. It has no curved sides, and all the lines are closed. The sum of the interior angles of a hexagon is 720 degrees. These shapes also have six rotational symmetries and six reflectional symmetries.
The picture below shows a regular hexagon.
There are three properties that a regular hexagon must have:
- All sides of the hexagon have to be equal in length.
- The interior angles must measure 120 degrees each.
- If you add all the interior angles together, they must equal 720 degrees.
Here’s an interesting fact:
You can split a hexagon up into six equilateral triangles. These will all be the same size and can fit back together like a honeycomb. When we do this with lots of hexagons, it’s known as tessellation.
What is an irregular hexagon shape?
An irregular hexagon has six sides and six angles that vary in length and size. This can lead to strange shapes you may not instantly recognize as hexagons. However, there are an infinite number of ways that you can align six sides to create a hexagon.
Here are a few different irregular-looking hexagons. Why don’t you try drawing a few more with your students?
How many sides does a hexagon have?
All hexagons have six sides, regardless of the type of hexagon. This means all have six sides: regular hexagons, concave hexagons, and convex hexagons.
How many angles does a hexagon have?
A hexagon has six angles because it has six vertices. Therefore, the interior angles of a regular hexagon add up to 720º, and each interior angle of a regular hexagon is 120º.
If your hexagon is irregular, all the angles could be different sizes. However, even if this is the case, they’ll still add up to720º.
Did you know that there are not just interior angles but exterior ones too?
Whereas the interior angles add up to720º, the exterior angles add up to 360º. You might be thinking that you’ve heard that number somewhere else. That’s because you have!
A circle is a 360º round. If you draw it correctly, you can fit a regular hexagon inside a circle. The corners of the hexagon should touch the circle six times round.
You might wonder who found out how many angles are in a hexagon. Well, it dates back to the Romans. In 36 BC, Roman philosophers were pondering the honeycomb hexagon shape. It turns out that it’s one of the most mathematically perfect forms. It’s also the most efficient packing method.
How many corners does a hexagon have?
Wondering how many corners a hexagon have? Well, since all hexagons have six sides, six vertices, and six angles, all hexagons have six corners too. This is always the case, and it does not matter what type of hexagon it is. So that means that regular hexagons, irregular hexagons, concave hexagons, and convex hexagons have six sides, six vertices, six angles, and six corners each.
Hexagon lines of symmetry
A regular hexagon has rotational symmetry. This means that when it is rotated on its axis, the shape of a regular hexagon looks the same. The rotation angle is 60°, and the order of the rotational symmetry is 6.
How symmetry lines does a hexagon have?
Regular hexagons have six lines of symmetry. You’ll find three along the lines that join the midpoints of its opposite sides and three more along the diagonals. This means that a regular hexagon has ‘reflection symmetry.’
To find a hexagon’s, or any shape’s, line(s) of symmetry, you must fold it. If the folded parts sit identically on top of each other, will all the edges match, then the fold line the line of symmetry? Some shapes have multiple lines of symmetry, like a regular hexagon, so fold the shape differently to see how many lines of symmetry it has.
Types of Hexagons
There are four main types of hexagons: regular, irregular, concave, and convex. We’ve already looked into the first two, so let’s investigate the latter.
What’s a concave hexagon?
A concave hexagon has an angle or angles that point inwards. If you measure this angle’s total, it will be more significant than 180 degrees.
This is the defining characteristic of a concave hexagon, and if your hexagon doesn’t have an inward pointing angle, it doesn’t count as a concave hexagon.
A concave hexagon has one line of symmetry across its middle. To check where the line of symmetry is on a concave hexagon, you must fold the shape in half horizontally, ensuring that all the corners are perfectly matched.
What is a convex hexagon?
A convex hexagon has no angles that point inwards, similar to a regular hexagon. Although both these types may look similar, make sure not to confuse them with each other, as a convex hexagon may not have sides of the same length or angle.
Plus, there are no lines of symmetry on a convex hexagon.
Where can I see hexagons in everyday life?
Do you think a specific shape, such as a hexagon, can appear in the world? If you look closely, you can see most shapes in everyday life. Here are a few examples of where you might find hexagons.
If you look closely, you can see most shapes in everyday life, but here are a few examples of where you might find hexagons:
- Beehives: The most common hexagons you’re probably thinking of are honeycombs in beehives. Bees are serious about being efficient; that’s why they make their honeycomb hexagon shaped. It’s a strong shape and doesn’t leave gaps between the holes like circles. You might think triangles also have those same qualities, but triangles don’t have enough space to store things and baby bees inside.
- Nuts: No, not the ones you eat! We’re talking about the nuts you use to fasten things. These are shaped like a hexagon with circular holes in the middle. They’re made like this because it makes them easier to turn with some tools. If they were a circle, lots of devices wouldn’t be able to grip onto them.
- Pencils: You might not have noticed, but your everyday pencils are hexagon-shaped. This is because it can save space when storing them, they’re easier to grip, and it makes gluing two halves together easier when manufactured.
- Saturn: You might be thinking, what does a planet have to do with hexagons? Isn’t a planet round? You’re right, but if you look at the top of Saturn, there’s a massive hexagon shape. It’s even bigger than Earth! Scientists think that this is an enormous storm with lots of different points of pressure. These points make the gasses form a hexagon shape.
- Footballs: Footballs include pentagons and hexagons stitched together into a sphere to make a round ball great for kicking. Take a look at your football the next time you have a PE lesson or a kickabout with your friends.
Don’t take our word for it; the next time you’re out there, see if you can spot some for yourself. You might be surprised by how many you find!
Properties of hexagons at a glance.
Here are a few properties and facts about hexagons:
- Every angle inside a regular hexagon is 120 degrees.
- Hexagon lines of symmetry: a regular hexagon has six axes of symmetry. Half of these pass through the diagonals that are opposite of the vertices. The others pass through the middle of the opposite edges.
- If you want to divide a hexagon up into equal parts, it’s easy. Just draw a line from the center to each of its vertices. This makes the hexagon look like a pizza with six perfect slices.
- If you divide a hexagon into six equal slices, each of the angles in the center would equal 60 degrees. These all add up to 360 degrees, forming a circle in the center of the regular hexagon.
- Fun fact: the New York supreme court in the USA is hexagon-shaped. It is the highest court in that state and has ultimate jurisdiction over criminal and civil cases.
