What is the name of a regular polygon with 6 sides?
The Correct Answer and Explanation is:
The name of a regular polygon with 6 sides is a regular hexagon.
A regular hexagon is a six-sided polygon where all sides are equal in length and all internal angles are equal in measure. The term “hexagon” comes from the Greek words hex, meaning six, and gonia, meaning angle. When the prefix “regular” is added, it specifies that not only does the shape have six sides, but that each side and angle is congruent with the others.
Each internal angle in a regular hexagon measures 120 degrees. This can be determined using the formula for the interior angle of a regular polygon:Interior angle=(n−2)×180∘n\text{Interior angle} = \frac{(n – 2) \times 180^\circ}{n}Interior angle=n(n−2)×180∘
For a hexagon, n=6n = 6n=6:Interior angle=(6−2)×180∘6=4×180∘6=120∘\text{Interior angle} = \frac{(6 – 2) \times 180^\circ}{6} = \frac{4 \times 180^\circ}{6} = 120^\circInterior angle=6(6−2)×180∘=64×180∘=120∘
The sum of the interior angles of any six-sided polygon, whether regular or irregular, is always 720 degrees. This is found using the formula:Sum of interior angles=(n−2)×180∘=4×180∘=720∘\text{Sum of interior angles} = (n – 2) \times 180^\circ = 4 \times 180^\circ = 720^\circSum of interior angles=(n−2)×180∘=4×180∘=720∘
A regular hexagon also has six lines of symmetry and rotational symmetry of order six. This means it looks the same after being rotated by 60 degrees, 120 degrees, and so on, up to 360 degrees.
Regular hexagons are commonly found in nature and design. Honeycomb cells made by bees are a natural example. The regular hexagon’s geometric efficiency allows for minimal material use while maximizing storage space. In mathematics, physics, and engineering, this shape is often used for its balance of strength and simplicity.
