Understanding Regular Polygons | Properties, Angles, and Symmetry in Geometry

regular polygon

A regular polygon is a two-dimensional figure that has equal side lengths and equal interior angles

A regular polygon is a two-dimensional figure that has equal side lengths and equal interior angles. In other words, all the sides and angles of a regular polygon are congruent (equal). Examples of regular polygons include equilateral triangles, squares, pentagons, hexagons, and so on.

The number of sides a regular polygon has is often denoted by “n”, and each interior angle of a regular polygon can be calculated using the formula: (n-2) × 180° / n. This formula works because the sum of all the interior angles of a polygon is always equal to (n-2) × 180°.

For instance, let’s consider a regular hexagon. It has six equal sides and six equal interior angles. Using the formula above, we can calculate the measure of each interior angle:

(n-2) × 180° / n = (6-2) × 180° / 6 = 4 × 180° / 6 = 120°

Therefore, each interior angle of a regular hexagon measures 120°.

Regular polygons have some interesting properties, such as their ability to tessellate (cover a plane without overlapping or leaving gaps). They also have a center point, called the circumcenter, which is equidistant from all its vertices. The length of the radius from the center to any vertex is called the circumradius, and it is the same for all regular polygons.

Overall, regular polygons exhibit a high degree of symmetry and are frequently used in mathematics and geometry.

More Answers: