A Shape With 7 Sides Is Called: Exploring The World Of Heptagons

What do you call a seven sided shape? Socratic from socratic.org

Welcome to our guide on heptagons, a fascinating shape that is often overlooked in the world of geometry. If you're wondering what a shape with 7 sides is called, the answer is simple: it's called a heptagon. But there's so much more to this shape than just its name. In this article, we'll explore the properties of heptagons, their real-world applications, and some interesting facts about them. Let's dive in!

What is a Heptagon?

A heptagon is a polygon with seven sides and seven angles. The word "heptagon" comes from the Greek words "hepta," meaning seven, and "gonia," meaning angle. Heptagons can come in many different shapes and sizes, but they all have one thing in common: they have seven sides.

Heptagons are a type of convex polygon, which means that all of their interior angles are less than 180 degrees. In fact, the sum of all interior angles in a heptagon is 900 degrees. This makes heptagons unique and interesting to study.

Properties of Heptagons

Angles

As we mentioned earlier, heptagons have seven angles. Since the sum of all interior angles in a heptagon is 900 degrees, each angle in a regular heptagon measures 128.57 degrees. However, not all heptagons are regular. In fact, most heptagons are irregular and have angles that vary in size.

One interesting fact about heptagons is that they can be used to create a tessellation, which is a pattern of shapes that fit together perfectly without any gaps or overlaps. To create a heptagon tessellation, you would need to create a regular heptagon and then tessellate it in a specific pattern.

Diagonals

A diagonal is a line segment that connects two non-adjacent vertices in a polygon. In a heptagon, there are a total of 14 diagonals. A regular heptagon has five diagonals that are equal in length, while an irregular heptagon has diagonals of varying lengths.

Diagonals are important in geometry because they can be used to calculate the area and perimeter of a polygon. In a heptagon, the length of the diagonals can be used to find the area of the shape using the formula:

Area = 7/4 x (diagonal length)^2 x cot(180/7)

Perimeter

The perimeter of a heptagon is simply the sum of all its sides. In a regular heptagon, all sides are equal in length, so you can find the perimeter by multiplying the length of one side by seven. In an irregular heptagon, the perimeter can be found by adding up the lengths of all seven sides.

Real-World Applications of Heptagons

While heptagons may not be as common as some other shapes, they still have many real-world applications. Here are just a few examples:

Stop signs: If you look closely at a stop sign, you'll notice that it's actually an octagon with one corner cut off. However, the shape that's left is a heptagon!

Crystals: Some crystals, such as garnets, naturally form in a heptagonal shape.

Music: The heptatonic scale, which is used in Western music, is based on the heptagon.

Interesting Facts about Heptagons

Here are some fun facts about heptagons:

The heptagon is the largest polygon that cannot be constructed using only a straightedge and compass.

The heptagon is also known as the septagon.

There is no regular heptagon that can be constructed using only a compass and straightedge.

Conclusion

Heptagons may not be as well-known as some other shapes, but they are still fascinating and worthy of study. From their unique properties to their real-world applications, there's a lot to learn about heptagons. We hope that this article has helped you understand more about this intriguing shape. Remember, a shape with 7 sides is called a heptagon, and it's just one of the many wonders of geometry.

So, next time you come across a heptagon in the wild, whether it's on a stop sign or in a crystal formation, you'll know exactly what it is!

Source: etc.usf.edu

Source: socratic.org

Source: byjus.com