Mastering Regular Polygons: Their Properties And Calculations

regular polygon

a polygon with all sides and all angles equal

A regular polygon is a 2D shape with straight edges and equal angles. It has equal sides and equal angles, and all its vertices lie on a common circle, which is referred to as the circumcircle.

The number of sides in a regular polygon determines its name. For example, a polygon with three sides is called a triangle, while a polygon with four sides is called a square.

Some important characteristics of regular polygons include:

– Interior angle: The measure of each interior angle of a regular polygon can be calculated using the following formula: (n – 2) x 180 / n, where n is the number of sides of the polygon. For example, the interior angle of a regular hexagon (six-sided polygon) would be (6 – 2) x 180 / 6 = 120 degrees.
– Exterior angle: The measure of each exterior angle of a regular polygon can be calculated using the formula 360 / n, where n is the number of sides of the polygon. For example, the exterior angle of a regular pentagon (five-sided polygon) would be 360 / 5 = 72 degrees.
– Perimeter: The perimeter of a regular polygon is the sum of its sides. For example, the perimeter of a regular octagon (eight-sided polygon) would be eight times the length of one side.
– Area: The area of a regular polygon can be calculated using different formulas depending on the information given. One common formula is A = (1/2) x apothem x perimeter, where the apothem is the perpendicular distance from the center of the polygon to a side. Another formula is A = (1/2) x perimeter x radius of circumcircle, where the radius is the distance from the center of the polygon to a vertex.

Regular polygons are used in many areas of geometry, such as in architecture, engineering, design, and art. They are often found in patterns and designs because of their symmetrical and aesthetically pleasing properties.

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