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The Fascinating World of Octagons

CEO Khai Intela
Have you ever wondered about the intriguing shape of an octagon? In geometry, an octagon is a polygon that has eight sides and eight angles. It's a two-dimensional figure that can be found in various...

Have you ever wondered about the intriguing shape of an octagon? In geometry, an octagon is a polygon that has eight sides and eight angles. It's a two-dimensional figure that can be found in various aspects of our lives. Let's delve into the world of octagons, exploring their properties, types, and real-life examples.

What is an Octagon?

An octagon is a closed two-dimensional shape with eight sides, eight vertices, and eight interior angles. If all the sides and interior angles of an octagon have the same measure, it is called a regular octagon. Otherwise, it is referred to as an irregular octagon. Octagons can also be categorized as convex or concave based on the orientation of their angles.

Octagon 1

Real-life examples of octagons are commonly seen in objects such as the outline of an umbrella with eight ribs, stop signs at intersections, and wall clocks with eight edges.

Octagon Sides and Angles

As the name suggests, an octagon has eight sides and eight angles. The angles can be divided into interior and exterior angles. The sum of the interior angles of an octagon is 1080 degrees, with each interior angle measuring 135 degrees. The sum of the exterior angles is 360 degrees, with each exterior angle measuring 45 degrees.

Properties of Octagons

When it comes to properties, regular octagons are usually considered. Here are some interesting facts about regular octagons:

  • Regular octagons have eight sides and eight angles.
  • All sides and angles of a regular octagon are equal.
  • A regular octagon contains a total of 20 diagonals.
  • The sum of the interior angles of a regular octagon is 1080 degrees.
  • The sum of the exterior angles of a regular octagon is 360 degrees.

Types of Octagons

Octagons can be classified into different types based on their sides and angles:

Regular and Irregular Octagons

A regular octagon has equal sides and equal angles. It possesses eight lines of symmetry and showcases perfect symmetry. On the other hand, an irregular octagon has unequal sides and unequal angles, lacking the same level of symmetry as a regular octagon.

Octagon 3

Convex and Concave Octagons

A convex octagon has all its angles pointing outward, with none of the angles exceeding 180 degrees. Conversely, a concave octagon has one of its angles pointing inward, creating a unique shape.

Octagon 4

Diagonals of Octagons

The number of diagonals in any n-sided polygon can be determined using the formula n(n - 3)/2. Applying this formula to an octagon (n = 8), we find that it contains a total of 20 diagonals.

Octagon 5

The length of the longest diagonal in a regular octagon can be calculated using the formula L = a√(4 + 2√2), where a represents the side length of the octagon.

Perimeter and Area of Octagons

The perimeter of an octagon is the sum of all its sides. For a regular octagon, the perimeter equals eight times the length of one side.

The area of an octagon is the region enclosed by its sides. The formula for the area of a regular octagon is 2a²(1 + √2), where a represents the length of one side.

Octagons in Everyday Life

Octagons can be found in various objects we encounter in our daily lives. From the outline of an umbrella to stop signboards at intersections, octagonal shapes are prevalent and play a significant role in our surroundings.

Conclusion

The fascinating world of octagons unveils the beauty and complexity of this intriguing shape. Whether it's the symmetrical regular octagon or the unique irregular octagon, these figures have captivated mathematicians and artists alike. Understanding the properties, types, and applications of octagons allows us to appreciate their presence in our environment. So, keep an eye out for octagons and admire the elegance they bring to the world around us.

Download BYJU’S-The Learning App to explore more fascinating geometrical concepts through engaging pictures and videos.

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