Decagon – Definition With Examples
Updated on January 8, 2024
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As we delve into the enchanting realm of decagons, you’ll discover their unique properties, fascinating realworld applications, and interesting mathematical aspects. By the end of this article, you’ll not only have a deeper understanding of decagons, but you’ll also appreciate the inherent beauty and elegance of mathematics.
So, let’s embark on this exciting journey together and unleash the math whiz within you! Here at Brighterly, we can’t wait to see you shine!
What Is a Decagon?
A decagon, at its core, is an aweinspiring polygon that boasts ten sides and ten angles, creating a captivating canvas for mathematical exploration. This closed, twodimensional geometric shape is formed by the seamless union of ten straight sides that meet at their endpoints. To visualize a decagon, simply imagine the harmonious fusion of a pentagon and a hexagon, culminating in an intricate, tensided masterpiece.
Decagons are not only mathematical marvels but also artistic wonders, as they make frequent appearances in various contexts, such as intricate patterns, architectural designs, and even nature itself. The mesmerizing properties of decagons, coupled with their fascinating applications, render them an exceptional subject for indepth investigation, especially for young, curious minds.
As we embark on this exciting adventure to unravel the mysteries of decagons, you’ll gain a newfound appreciation for the elegance and complexity that lies within these tensided gems. Through our exploration of the diverse world of decagons, we’ll unveil their hidden secrets, unmasking the intricate tapestry of mathematics that weaves them together. So join us on this thrilling quest as we uncover the remarkable world of decagons, and unleash the mathematician within you!
Meaning of Decagon
The term decagon comes from the Greek words “deka,” which means ten, and “gonia,” which means angle. So, when you hear the word “decagon,” you can think of it as a shape with ten angles. These ten angles are created by the ten sides that form the polygon, and their sum is always equal to 1,440 degrees.
Types of Decagon
Delving deeper into the fascinating realm of decagons, we discover that these tensided wonders can be categorized into two distinct types, each with its unique characteristics and properties:

Regular Decagon: A decagon earns the title of “regular” when all its ten sides are of equal length, and all its ten angles possess equal measures. The hallmark of a regular decagon is its perfect symmetry, where each angle measures precisely 144 degrees. This harmonious balance results in a geometric shape that exudes elegance and mathematical beauty.

Irregular Decagon: Contrasting with its regular counterpart, an irregular decagon features unequal side lengths and unequal angle measures. While still retaining its defining feature of ten sides and ten angles, the irregular decagon deviates from the symmetrical perfection of a regular decagon, giving rise to a more diverse and unpredictable array of shapes.
Solved Examples
To better comprehend the intricacies of decagons, let’s delve into a few solved examples that showcase their unique properties and mathematical relationships:

Area of a Regular Decagon: To calculate the area
A
of a regular decagon, given its side lengtha
, we employ the following formula, which elegantly combines geometry and trigonometry:A = (5a²) / (4 * tan(π/10))
This formula allows us to determine the area enclosed by a regular decagon, revealing the relationship between its side length and the overall space it occupies.

Perimeter of a Decagon: Calculating the perimeter
P
of a decagon, whether regular or irregular, is a straightforward process, as it simply involves summing up all its side lengths. This value represents the total distance around the decagon, providing insight into its size and scale in relation to its individual sides.
By examining these examples and deepening our understanding of decagons, we can begin to appreciate the complex interplay of mathematical principles that govern these remarkable geometric shapes.
Properties of Decagon
As we continue to explore the enchanting world of decagons, let’s unravel some of their most intriguing properties, which make them a captivating subject of study for math enthusiasts and artists alike:
 A decagon inherently possesses ten sides and ten angles, giving rise to its unique shape and symmetry.
 The sum of the interior angles of a decagon always amounts to a remarkable 1,440 degrees, highlighting the underlying mathematical relationships between its angles.
 A decagon can be artistically dissected into eight triangles by skillfully drawing nonintersecting diagonals from a single vertex. This process reveals the hidden geometric patterns and relationships within the decagon.
 The total number of diagonals in a decagon is an impressive 35, further illustrating the intricate web of connections that exist within its structure.
 A regular decagon is characterized by its equal side lengths and equal angle measures, which contribute to its harmonious and symmetrical appearance.
Decagon Examples
Decagons are not confined to the realm of mathematics; they can be found in a multitude of everyday scenarios and various fields of study, showcasing their beauty and versatility:
 In the world of architecture, decagonal buildings such as the Bahá’í House of Worship in Wilmette, Illinois, stand as a testament to the elegance and aesthetic appeal of this geometric shape.
 Decagonal patterns frequently grace the halls of Islamic art and architecture, adorning the intricate tiling of the Alhambra Palace in Spain and contributing to its breathtaking beauty.
 Mother Nature, too, has a penchant for decagons, as evidenced by the radial symmetry of certain flowers and starfish, which incorporate this tensided wonder into their mesmerizing designs.
By examining these realworld examples of decagons, we can gain a deeper appreciation for their allure, as well as the intricate tapestry of mathematics that governs their existence.
Practice Questions on Decagon
Armed with your newfound knowledge about decagons, it’s time to put your understanding to the test! Dive into these practice questions and challenge yourself to solve the mysteries of these captivating tensided figures:
 Area of a Regular Decagon: Calculate the area of a regular decagon with a side length of 6 cm. Remember to use the formula A = (5a²) / (4 * tan(π/10)) to determine the area enclosed by this symmetrical shape.
 Perimeter of an Irregular Decagon: Find the perimeter of an irregular decagon with side lengths of 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 cm. To calculate the perimeter, simply add up the lengths of all ten sides.
 Angle Measures in a Regular Decagon: If one angle of a regular decagon measures 144 degrees, what is the measure of each of the other nine angles? Recall that all angles in a regular decagon are equal, which will help you find the answer.
 Triangles Formed by Diagonals: Determine the number of triangles that can be formed by drawing diagonals from one vertex of an irregular decagon. To solve this problem, think about how many nonintersecting diagonals can be drawn and how they divide the decagon into triangles.
By tackling these practice questions, you’ll solidify your understanding of decagons and their intriguing properties, further honing your mathematical skills and nurturing your love for geometry. So, go ahead and challenge yourself – the world of decagons awaits!
Conclusion
Decagons, with their captivating charm and mesmerizing properties, are truly fascinating geometric shapes that have left their indelible mark in art, architecture, and the natural world. By delving into their characteristics and uncovering their secrets, you not only develop a deeper appreciation for the beauty and complexity of mathematics, but also immerse yourself in the enchanting world of geometry. At Brighterly, our goal is to ignite that spark of curiosity within you and guide you on this incredible journey of discovery.
We sincerely hope that this article has not only piqued your interest in decagons but has also provided you with a strong foundation for further exploration. As you continue to uncover the mysteries of these tensided marvels, you’ll undoubtedly find yourself entranced by their elegance and symmetry, and inspired to explore other captivating aspects of mathematics.
So, as you embark on your mathematical adventures with Brighterly, remember that the world is full of wondrous shapes and patterns just waiting to be discovered. Keep learning, keep growing, and keep shining brightly, for the world of mathematics is vast and full of endless possibilities!
Frequently Asked Questions on Decagon
As we wrap up our exploration of the fascinating world of decagons, let’s address some frequently asked questions that often arise when discussing these tensided wonders. By answering these queries, we hope to solidify your understanding of decagons and their unique properties.
How many sides does a decagon have?
A decagon boasts an impressive ten sides, which give it its distinct shape and symmetry.
What is the difference between a regular and an irregular decagon?
The key distinction between a regular and an irregular decagon lies in their side lengths and angle measures. A regular decagon is characterized by equal side lengths and equal angle measures, resulting in perfect symmetry. In contrast, an irregular decagon features unequal side lengths and unequal angle measures, leading to a more diverse array of shapes and configurations.
What is the sum of the interior angles of a decagon?
The sum of the interior angles of a decagon always amounts to a remarkable 1,440 degrees, showcasing the intricate mathematical relationships between its angles.
How can I calculate the area of a regular decagon?
To determine the area of a regular decagon, you can employ the formula A = (5a²) / (4 * tan(π/10)), where a
represents the length of one side. This formula artfully combines geometry and trigonometry to reveal the relationship between the decagon’s side length and the overall space it occupies.
Can decagons be found in the real world?
Absolutely! Decagons make their presence known in a variety of contexts, such as the stunning architecture of the Bahá’í House of Worship in Illinois, the intricate tiling of the Alhambra Palace in Spain, and even the radial symmetry of certain flowers and starfish. These examples demonstrate the versatility and allure of decagons, both in the world of mathematics and beyond.
By addressing these frequently asked questions, we hope to enhance your understanding of decagons and inspire you to continue exploring the rich tapestry of mathematics that surrounds us. Remember, at Brighterly, our mission is to make math an enjoyable and captivating adventure for young learners like you!