Heptagon – Definition with Examples

Welcome to another exciting topic on Brighterly, the best place for math-loving children! In today’s article, we will learn about heptagons. Get ready to explore the wonderful world of seven-sided polygons, as we dive into their properties, types, formulas, and more! Together with Brighterly’s interactive and engaging content, we will make understanding heptagons a fun and memorable experience for kids of all ages.

What is a Heptagon?

A heptagon is a closed geometric figure with exactly seven sides and seven angles. The word “heptagon” comes from the Greek words “hepta” meaning seven, and “gonia” meaning angle. Just like triangles, quadrilaterals, and pentagons, heptagons are also classified as polygons, which are shapes formed by connecting straight lines. Heptagons can be found in various forms in the world around us, from natural occurrences to man-made designs. Learning about heptagons is an excellent opportunity for children to enhance their spatial reasoning and critical thinking skills, and with Brighterly, it’s as enjoyable as it is educational!

Properties of Heptagon

A heptagon has some unique properties that set it apart from other polygons. With Brighterly’s focus on making math concepts accessible for kids, we will discuss these properties in an easy-to-understand manner:

  1. Seven Sides and Angles: A heptagon has 7 sides and 7 angles, making it instantly recognizable from other polygons. This unique structure adds a level of complexity that challenges kids to think more critically about geometric shapes.

  2. Sum of Interior Angles: The sum of the interior angles of a heptagon is (7-2) * 180° = 900°. This property helps kids understand the relationships between the angles and how they can be used to solve various problems.

  3. Exterior Angles: The exterior angles of a heptagon always add up to 360°. This property allows children to gain a deeper understanding of angle relationships in polygons and can be applied in real-world situations and problem-solving tasks.

By exploring these properties, children can develop a strong foundation in geometry and prepare themselves for more advanced math concepts in the future. And with Brighterly’s engaging content and approach, learning about heptagons becomes an enjoyable and enriching experience for kids.

Types of Heptagon

Heptagons come in various shapes and sizes, and understanding their different types helps kids appreciate the diversity and complexity of geometric figures. With Brighterly’s focus on making math engaging and relatable, we will explore the main types of heptagons and their unique characteristics:

  1. Regular Heptagon: All the sides and angles of a regular heptagon are equal, creating a symmetrical and visually appealing shape. The interior angles of a regular heptagon measure 128.57° each. Regular heptagons are excellent for introducing kids to the concept of symmetry in geometry and provide an opportunity to explore various properties and patterns in polygons.

  2. Irregular Heptagon: An irregular heptagon has unequal sides and angles, resulting in a diverse range of shapes and forms. There are no specific rules for the measurements of sides and angles in an irregular heptagon, which encourages children to think creatively and use their imagination. Irregular heptagons help kids understand that not all polygons follow strict patterns, and they offer a chance to explore the endless possibilities in geometry.

Concave and Convex Heptagon

Another way to categorize heptagons is based on their angles, which leads us to concave and convex heptagons. With Brighterly’s child-friendly approach, we will delve into the unique features of these heptagon classifications:

  1. Concave Heptagon: At least one of the interior angles in a concave heptagon measures more than 180°. As a result, it appears to have a “caved-in” or “dented” side. Concave heptagons provide an excellent opportunity for kids to explore the concept of angles greater than 180° and help them visualize how such angles affect the shape of a polygon.

  2. Convex Heptagon: All the interior angles of a convex heptagon are less than 180°, which gives it a smooth, outward appearance without any indentations. Convex heptagons are useful for teaching kids about angle relationships and the importance of angles in defining a polygon’s shape.

Regular Heptagon Formula

For a regular heptagon, we can calculate the side length (s), perimeter (P), and area (A) using the following formulas. Brighterly’s goal is to make these mathematical concepts easy to understand for kids, so they can apply these formulas in their math practice with confidence:

  1. Perimeter (P): P = 7s (where s is the length of a side). This formula shows how the perimeter of a regular heptagon is directly related to its side length, making it easy for kids to calculate the perimeter when given the side length.

  2. Area (A): A = (7s²) / (4 * tan(180° / 7)). While this formula may appear complex, it helps kids understand the importance of trigonometric functions in geometry and encourages them to use a scientific calculator to find the area of a regular heptagon accurately.

Perimeter of a Heptagon

To find the perimeter of a heptagon, simply add the lengths of all its sides. For a regular heptagon, multiply the side length by 7.

Area of a Heptagon

Calculating the area of an irregular heptagon can be complex. However, for a regular heptagon, you can use the formula mentioned earlier: A = (7s²) / (4 * tan(180° / 7))


Heptagons are fascinating polygons with unique properties and applications, providing a rich learning opportunity for children of all ages. By understanding their characteristics, types, and formulas, kids can expand their mathematical knowledge and problem-solving skills in a fun and engaging way. At Brighterly, we are committed to making math enjoyable and accessible for every child, and we hope you enjoyed learning about heptagons with us today!

As you continue your journey with Brighterly math for kids, you will discover more exciting math topics that will challenge your mind and spark your curiosity. Remember, practice is the key to mastering any math concept, so don’t forget to check out our amazing collection of worksheets math for kids to reinforce your understanding of heptagons and other geometric shapes.

Stay curious, keep exploring, and have fun with math! We look forward to accompanying you on your learning journey with Brighterly.

FAQs on Heptagon

What is a heptagon?

A heptagon is a polygon with seven sides and seven angles. It is classified as a closed geometric figure formed by connecting straight lines.

What are the types of heptagons?

Heptagons can be classified into four main categories: regular, irregular, concave, and convex. Regular heptagons have equal sides and angles, while irregular heptagons have unequal sides and angles. Concave heptagons have at least one interior angle greater than 180°, while convex heptagons have all interior angles less than 180°.

What is the sum of interior angles in a heptagon?

The sum of the interior angles in a heptagon is 900°. You can find this by using the formula (n – 2) * 180°, where n represents the number of sides.

What is the measure of each interior angle in a regular heptagon?

In a regular heptagon, each interior angle measures approximately 128.57°. You can calculate this by dividing the sum of the interior angles (900°) by the number of angles (7).

What is the measure of each exterior angle in a regular heptagon?

Each exterior angle in a regular heptagon measures approximately 51.43°. You can find this by dividing the total sum of exterior angles (360°) by the number of angles (7).

How do you find the perimeter and area of a regular heptagon?

To find the perimeter (P) of a regular heptagon, use the formula P = 7s, where s is the length of a side. To find the area (A), use the formula A = (7s²) / (4 * tan(180° / 7)).

Are there any real-world examples of heptagons?

While heptagons are less common than other polygons, they can be found in various forms in the world around us, such as in architecture, design patterns, logos, and even some naturally occurring crystals.

Remember, if you have more questions or need further clarification, you can always refer back to this article or explore additional resources on Brighterly.

Information Sources

Some sources of information for this article include:

  1. Wikipedia – Heptagon
  2. Mathworld – Heptagon
  3. Wolfram Alpha – Heptagon

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