A hexagon is a polygon with six sides and six angles. In a regular hexagon, all sides and angles are equal. The sum of the interior angles of a hexagon is 720°, and each interior angle of a regular hexagon is 120°.
Below is the figure of a Hexagon with six vertices(A, B, C, D, E, F):
Here are a few key properties:
- Sides: 6
- Interior Angles: 120° each (for a regular hexagon)
- Exterior Angles: 60° each (since exterior angles are supplementary to interior angles)
- Symmetry: A regular hexagon has rotational symmetry of order 6 and reflectional symmetry along 6 axes.
Hexagons are commonly seen in nature, such as in honeycombs, and have useful properties in tiling and packing.
Real-Life Examples of Hexagon
Hexagon is often seen in nature, animals, and geological patterns, some examples are:
- Honeycombs
- Carbon Nanotubes
- Snowflakes
- Digital Displays
- Basalt Columns
Properties of Hexagon
Some of the Properties of Hexagon are:
- It is a polygon with six straight sides and six vertices.
- Sum of the interior Angles of a hexagon is always 720°.
- A regular hexagon has a total of nine diagonals.
- Each exterior angle of a regular hexagon is 60° (since the exterior angle is 360°/6 = 60°).
- For all hexagons, the sum of all external angles is 360 degrees.
Types of Hexagon
There are primarily 5 main types of Hexagons as shown in the image below:
Regular Hexagon
- Properties: All sides and angles are equal.
- Angles: Each interior angle is 120°.
- Symmetry: Has six lines of symmetry and rotational symmetry of order 6.
- Example: A honeycomb cell.
Irregular Hexagon
- Properties: The sides and angles are not all equal.
- Angles: The sum of the interior angles is always 720°, but individual angles vary.
- Symmetry: May have limited or no symmetry.
- Example: A randomly shaped tile in a design.
Concave Hexagon
- Properties: Has at least one interior angle greater than 180°.
- Angles: Some interior angles are greater than 180°, making the shape "dented" or "inward."
- Symmetry: Typically lacks symmetry.
- Example: A star-shaped hexagon.
Convex Hexagon
- Properties: All interior angles are less than 180° and all vertices point outward.
- Angles: All interior angles are less than 180°, which keeps the shape outwardly curved.
- Symmetry: Typically symmetrical.
- Example: A hexagonal-shaped gemstone.
Complex Hexagon
- Properties: A hexagon with irregular sides, angles, or self-intersecting edges.
- Angles: Interior angles may vary, with some greater than 180° (concave).
- Symmetry: May have limited or no symmetry.
- Example: A star-shaped self-intersecting hexagon.
Hexagon Geometry Formulas
The formula for the Area and Perimeter of a Regular Hexagon is mentioned below:
Area of Hexagon
The formula for the area of a Regular Hexagon with side s is:
Area = (3√3s2)/2
Perimeter of Hexagon
The formula for the Perimeter of a Regular Hexagon is
Perimeter = 6s
Read More: Hexagon Formula
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