Exploring Regular Polygons | Definition, Properties, and Formulas

regular polygon

A regular polygon is a polygon that has equal sides and equal angles

A regular polygon is a polygon that has equal sides and equal angles. In other words, all of its sides and angles are congruent. The sides of a regular polygon are all the same length, and the angles between adjacent sides are all the same measure.

A regular polygon can have any number of sides, but some common examples are the equilateral triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), heptagon (7 sides), octagon (8 sides), and so on. The names of regular polygons are derived from Greek or Latin words indicating the number of sides they have.

One key property of regular polygons is that they can be perfectly circumscribed or inscribed within a circle. This means that all vertices of the polygon lie on the circumference of a circle or that the sides of the polygon are tangent to a circle. The center of this circle coincides with the center of the polygon.

The formula to calculate the interior angle of a regular polygon is:
(interior angle) = (n-2) * 180 / n,
where n represents the number of sides of the polygon. This formula gives you the measure in degrees of each interior angle of the polygon.

In addition, the formula to determine the sum of the interior angles of a regular polygon is:
(sum of interior angles) = (n-2) * 180,
which gives you the total measure in degrees of all the interior angles of the polygon.

Regular polygons have symmetry properties due to their congruent sides and angles. They possess rotational symmetry, meaning that you can rotate the polygon around its center point by a certain angle and still obtain the same shape. The degree of rotational symmetry depends on the number of sides the polygon has. For example, a square has rotational symmetry of 90 degrees and a hexagon has rotational symmetry of 60 degrees.

Overall, regular polygons are geometric figures that exhibit uniformity in both their sides and angles. They have many interesting mathematical properties and are frequently encountered in various fields such as geometry, architecture, art, and design.

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