Understanding Regular Polygons | Properties, Formulas, and Applications

regular polygon

A regular polygon is a polygon that has all of its sides and angles equal in measure

A regular polygon is a polygon that has all of its sides and angles equal in measure. In other words, all the sides of a regular polygon have the same length, and all the angles have the same degree measure. Examples of regular polygons include equilateral triangles, squares, pentagons, hexagons, and so on.

To determine the properties of a regular polygon, we need to know the number of sides it has, denoted by “n”. Each regular polygon can be classified based on the number of sides it possesses. For example:
– A regular polygon with 3 sides is called an equilateral triangle.
– A regular polygon with 4 sides is called a square.
– A regular polygon with 5 sides is called a pentagon.
– A regular polygon with 6 sides is called a hexagon.
– And so on.

Regular polygons have specific formulas to calculate their properties:
1. Interior angle: The measure of each interior angle of a regular polygon can be found using the formula:
Interior Angle = (n-2) * 180° / n
where “n” is the number of sides of the polygon.

2. Exterior angle: The measure of each exterior angle of a regular polygon can be calculated by subtracting the interior angle from 180°:
Exterior Angle = 180° – Interior Angle

3. Sum of interior angles: The sum of all the interior angles of a regular polygon can be calculated using the formula:
Sum of Interior Angles = (n-2) * 180°
Here, “n” represents the number of sides of the polygon.

4. Sum of exterior angles: The sum of all the exterior angles of a regular polygon is always 360°.

Regular polygons have various real-life applications, such as in architecture, art, design, and even in nature (e.g., honeycomb structures). They have symmetrical shapes and are widely studied in geometry due to their well-defined properties.

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