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The Fascinating Heptagon: Discovering the Secrets of the Seven-Sided Polygon

CEO Khai Intela
Image: Types of polygons When it comes to shapes, polygons are the building blocks of geometry. From triangles to squares and hexagons, each polygon has its own unique properties and characteristics. Today, we're diving into...

Types of polygons Image: Types of polygons

When it comes to shapes, polygons are the building blocks of geometry. From triangles to squares and hexagons, each polygon has its own unique properties and characteristics. Today, we're diving into the intriguing world of the heptagon, a seven-sided polygon that is often referred to as the septagon.

What is a Heptagon?

Heptagon Image: Heptagon

A heptagon is a polygon with seven sides and seven angles. It is a closed figure where each side meets end to end, forming a distinct shape. The number of sides is what sets the heptagon apart from other polygons, such as triangles, quadrilaterals, and hexagons.

Exploring Heptagon Shapes

There are different types of heptagons based on their angles and diagonals:

Regular and Irregular Heptagon

A regular heptagon has equal side lengths and angles. The sides of a regular heptagon meet at an angle of 5π/7 radians or approximately 128.57 degrees. On the other hand, an irregular heptagon has sides and angles of different measures.

Regular and Irregular Heptagon Image: Regular and Irregular Heptagon

Convex and Concave Heptagon

A convex heptagon is one where all the diagonals lie inside the shape. In contrast, a concave heptagon has some diagonals that extend outside the polygon, creating one or more interior angles greater than 180 degrees.

Unveiling Heptagon Properties

Here are some interesting properties of heptagons:

  • The sum of the interior angles of a heptagon is 900 degrees.
  • The sum of the exterior angles of a heptagon is 360 degrees.
  • In a regular heptagon, each interior angle measures approximately 128.57 degrees.
  • The measure of the central angle of a regular heptagon is approximately 51.43 degrees.
  • A heptagon has 14 diagonals.
  • Regular heptagons are also known as convex heptagons.
  • A heptagon forms 5 different triangles.

Calculating Heptagon Area and Perimeter

To find the area of a regular heptagon with a side length "a," we can use the following formula:

A = 3.634a² square units

The perimeter or circumference of a regular heptagon is simply:

P = 7a units

Let's solve a problem to illustrate this:

Heptagon Solved Problem

Question: Find the area and perimeter of a regular heptagon with a side length of 5 cm.

Solution: Given: Side length (a) = 5 cm

Using the formula for the area of a heptagon:

A = 3.634a² A = 3.634(5)² A = 3.634(25) A ≈ 90.85 cm²

Therefore, the area of the heptagon is approximately 90.85 cm².

To find the perimeter of the heptagon:

P = 7a P = 7(5) P = 35 cm

Hence, the perimeter of the heptagon is 35 cm.

Now you have a deeper understanding of the heptagon, one of the fascinating polygons in geometry. If you want to explore more intriguing math concepts, remember to stay tuned with BYJU'S - The Learning App. Happy learning!

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