Tatiana enjoys creating useful, everyday resources for children and adults alike. Education is her passion.
An Introduction to Polygons
When it comes to learning shapes, it’s really helpful to know how many sides each one has. Not only will knowing this vital piece of information help you with shape recognition, but it can also make you look pretty smart! In this article, we'll start with the most basic polygonal shapes and work our way up to the more complicated ones you likely haven’t heard of before!
Also included (at the bottom of this article) is an easy reference table that lists all polygons with sides numbering 3 to 30.
Triangle: 3 Sides
The triangle is a very distinctive shape, only ever consisting of three sides connected together. If you ever see a shape that has three sides, it cannot be anything else but a triangle. Some things that are shaped like a triangle are a yield sign, a wedge, a side of a pyramid, a pool game rack, and of course, the triangle instrument.
The name triangle literally means three angles. Anytime you see the prefix of "tri," you should think "three." The triceratops was a dinosaur with three horns, a tricycle is a bike with three wheels, and a trio is a group of three people.
Quadrilateral (Square, Rectangle): 4 Sides
A quadrilateral is any polygon with four sides. A square is a quadrilateral and a parallelogram that has four equal sides that come together at right angles. If the sides are not the same size and/or are not parallel, then it is not a square! Examples of common items that are often square include baking pans, couch pillows, patio tables, and ottomans. Please note that these items can also be rectangles! Adding to that, a square is considered a rectangle, but a rectangle can never be a square. Sad, I know.
A rectangle is also a parallelogram with four sides coming together at right angles, but unlike the square, two of its sides are longer than the other two. Because of this, the shape has an elongated look when compared to a square. Even one pair of sides is only slightly longer than the pair in a quadrilateral, it is still considered a rectangle and not a square. Often times, dinner tables, sports fields, the perimeters of basic houses, picture frames, and books are rectangular
Pentagon: 5 Sides
A pentagon is any polygon that has five sides. The simple pentagon has five equal sides that join to their neighboring sides at equal angles. A concave pentagon is made with two of the sides pointing inward to form a v-shaped point toward the other sides rather than pointing out in a convex manner. A pentagram is an example of a self-intersecting pentagon, as it is made of five lines, but they cross over one another to form a star shape. A popular example of the basic pentagon shape is the Pentagon, a governmental building in Washington, D.C.
Hexagon: 6 Sides
A hexagon has six sides and six vertices, or points. The interior angles of a hexagon add up to 720 degrees. The most common hexagon is the regular hexagon, in which all of the sides are the same length. Perhaps the most recognizable hexagon-shaped item in life is a common piece of hardware known as a nut. Zebra cakes are also shaped like hexagons, and the Star of David is considered a self-intersecting hexagon.
Octagon: 8 Sides
Octagons have eight sides. A regular octagon is a shape consisting of eight even sides in which the interior angles add up to 1080 degrees. Chances are you’ve seen many stop signs in your day, which means you’ve seen an octagon before your very eyes! If you are a fan of the UFC (Ultimate Fighting Championship), then you are probably aware that participants in the sport fight in an octagon-shaped ring. The prefix "oct" refers to the number eight, so it makes sense that an octopus has eight tentacles and an octet is a group of eight.
Decagon: 10 Sides
Decagons have 10 sides, and in regular decagons, all of the sides are of even lengths. Although not commonly thought of as a decagon, the perimeter of a five-pointed star is technically a decagon. The Gonbad-e Qabus tower in Iran is a well-known building that has this shape. It also makes use of the golden ratio and has stood for over 1,000 years! Or 100 dec-ades! See what I did there? The prefix of dec usually denotes the number 10, such as decagon (10 sides), decade (10 years), decaliter (10 liters), or deciliter (1/10th of a liter).
Dodecagon: 12 Sides
Not to be confused with a decagon, a dodecagon has just two more sides for a total of 12. 12 sides and 12 angles make this shape unique from the others. As you can see, the name is very similar to "decagon" which has 10 sides. The "do" prefix just means add 2 to 10 which gives you 12. Pretty easy, right? That means a tridecagon would have how many sides? "Tri" means 3 and "dec" means 10, so a tridecagon would have 13 sides.
Triacontagon: 30 Sides
I’m going to skip ahead now to the 30-sided figure called the triacontagon because at this point, it almost begins to look like a circle! Notice the “tri” (meaning three) in the beginning of the name, which helps indicate the number of sides to the figure.
While it is a bit more of an advanced subject, as you approach an infinite number of sides, the shape begins to look more and more like a circle. In fact, computers can't actually draw a true circle. They draw what looks like a circle but is really just a polygon. Don't believe me? Just zoom in a bunch on a circle you see on your screen, and chances are, you'll see a very rough looking shape once you get in close enough.
How Do Shape Names Work?
You may recall some of these harder shapes from geometry class. Regardless, now you have been schooled and/or refreshed in the topic!
Below is a table that makes looking up a shape's name and the number of sides it has really simple. You can also see the pattern in how the names are made, and you can probably start to figure out what the names of certain polygons are without ever having to look them up.
One important thing to know—rather than committing all of these names to memory, it is acceptable to use the shorthand. Many mathematicians will refer to polygons with a lot of sides using the "n-gon" shorthand, where "n" is the number of sides. So, you can call a polygon with 13 sides can be called a 13-gon instead of a tridecagon, and people won't look at you funny (or if they do, it will be because they have no idea what you're talking about.
Shapes and Number of Sides
|Shape Name||Number of Sides|
This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.
poetryman6969 on February 07, 2015:
I think there was a story that a famous artist drew a perfect circle free hand. The notion being that perfection in anything is strong message. Some would go so far as to say if we ever meet an alien race and their first act to hand us something made at a level of perfection that is beyond us, we are in a lot of trouble.