Side of a Polygon

A polygon shape is any geometric shape which is classified by their number of sides and is enclosed by a number of straight sides. However, a polygon is considered regular when each of its sides measure equal in length. For example, a 3-sided polygon is a triangle, an 8 -sided polygon is an octagon, while an 11 sided polygon is called 11-gon or hendecagon. The number of sides of a regular polygon can be computed with the help of interior and exterior angles.

Names of Polygons

Convex and Concave Polygons

A convex polygon closes in an interior space without appearing "dented." None of the interior angles pointing inward. In geometrical math, you could have a 4-sided polygon which points outward in all directions, like a kite, or you could have similar four sides so two of them point inward, creating a dart. The dart is concave and the kite is convex.

Each interior angle of a convex polygon measures less than 180°. A concave polygon has a minimum of one angle greater than 180°. Imagine a bowtie-shaped hexagon (6 sides). It will consist of two interior angles greater than 180°.

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Simple and Complex Polygons

Simple polygons contain no self-intersecting sides. Complex polygons, also known as self-intersecting polygons, contain sides that cross over each other. An example of a complex polygon is a classic star. Most people can sketch a star on a sheet of paper very quickly, but some people label it a pentagram, complex polygon, or self-bisecting polygon.

The family of complex star-shaped polygons usually share the Greek number prefix and use the suffix -gram: pentagram, hexagram, heptagram, octagram, and so on.

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Solved Examples on a Polygon Shape

Example:

Find out the Interior Angle of a Regular Octagon?

Solution:

A regular octagon consists of 8 sides, thus:

Exterior Angle of an octagon = 360° / 8 = 45°

Interior Angle of an octagon = 180° − 45° = 135°

Or we could also use the formula to determine the interior Angle of an octagon:

Interior Angle = (n−2) × 180° / n

= (8−2) × 180° / 8

= 6 × 180° / 8

= 135°

Thus, the Interior Angle of an octagon measures 135°

Example:

Determine the Interior and Exterior Angles of a Regular Hexagon?

Solution:

A regular hexagon consists of 6 sides, thus:

Exterior Angle of a hexagon= 360° / 6 = 60°

Interior Angle of a hexagon = 180° − 60° = 120°

Fun Facts

• Interior and exterior angles of a polygon are respectively, the inside and outside angles formed by the connecting sides of the polygon.

• To be a polygon, the shape must be flat, circumscribed in space, and be created using only straight sides.

• Polygons with congruent angles and sides are regular; while all others are irregular.

• Polygons with all interior angles measuring less than 180° are convex

• Polygon having a minimum of one interior angle greater than 180° is concave.

• Simple polygons don’t cross their sides

• Complex polygons have self-bisecting sides.

• You can spot Polygons all around you!

Conclusion

Polygons can be studied and categorized in different ways. You can see that polygons can be regular or irregular, concave or convex, and simple or complex. When you come across an unfamiliar polygon, you can simply identify its properties and classify it correctly.