The Sum Of Interior Angles Of A Hexagon: Explained
Hexagons are six-sided polygons that have been fascinating mathematicians for centuries. One of the most interesting properties of hexagons is their interior angles' sum, which we will explore in this article. Whether you're a student, a teacher, or just someone interested in geometry, read on to learn more about the sum of interior angles of a hexagon.
What is a Hexagon?
Before we dive into the sum of interior angles of a hexagon, let's first define what a hexagon is. A hexagon is a six-sided polygon with six angles. Each angle in a hexagon measures 120 degrees, and the sum of all six angles is 720 degrees. Hexagons can be regular or irregular, convex or concave, and can have different side lengths and shapes.
How to Find the Sum of Interior Angles of a Hexagon?
To find the sum of interior angles of a hexagon, we can use a simple formula. The formula to find the sum of interior angles of a hexagon is:
Sum of interior angles of a hexagon = (n-2) x 180 degrees
Where n is the number of sides of the polygon, which in this case is 6 for a hexagon. Substituting the value of n in the formula, we get:
Sum of interior angles of a hexagon = (6-2) x 180 degrees = 4 x 180 degrees = 720 degrees
Therefore, the sum of interior angles of a hexagon is 720 degrees, which is also the sum of all its angles.
Proof of the Sum of Interior Angles of a Hexagon
Now that we know the formula to find the sum of interior angles of a hexagon, let's take a deeper look at why it works. To prove the formula, we can divide a hexagon into triangles, as shown in the figure below:
As we can see in the figure, a hexagon can be divided into four triangles, each with an interior angle of 60 degrees. Therefore, the sum of the interior angles of the four triangles is:
Sum of interior angles of four triangles = 4 x 180 degrees = 720 degrees
But this sum includes the three interior angles of the hexagon's center, which add up to 180 degrees. Therefore, the sum of the hexagon's interior angles is:
Sum of interior angles of a hexagon = Sum of interior angles of four triangles - Sum of three interior angles of center = 720 degrees - 180 degrees = 540 degrees
Therefore, the sum of interior angles of a hexagon is 540 degrees, which is also equal to (6-2) x 180 degrees.
Real-Life Examples of Hexagons
Hexagons are not just a mathematical concept, but they also exist in the real world. Here are some examples of hexagons in nature and human-made objects:
- Honeycomb cells: The cells of a honeycomb are hexagons, which bees use to store honey and raise their young.
- Snowflakes: Snowflakes have a hexagonal shape due to the way water molecules bond together when they freeze.
- Soccer ball: A soccer ball is made up of 20 hexagons and 12 pentagons, which form a polyhedron called an icosahedron.
- Tiles: Hexagonal tiles are a popular choice for flooring and backsplashes in homes and public buildings.
Conclusion
In conclusion, the sum of interior angles of a hexagon is a fascinating mathematical concept that has practical applications in various fields. We learned that the sum of interior angles of a hexagon is 720 degrees, and we also saw how this formula can be proved using a simple geometric method. We hope this article has helped you understand the sum of interior angles of a hexagon better and appreciate the beauty of geometry.
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