Equalsided

Equalsided is a geometric term used to describe figures whose sides are all the same length. In polygonal geometry, an equalsided polygon is more commonly called an equilateral polygon. The defining property is that every edge has the same length; the interior angles are not specified and may vary.

Examples and scope: An equalsided triangle is the equilateral triangle, in which all three sides are equal and each interior angle is 60 degrees. In quadrilaterals, a shape with all sides equal is a rhombus; its angles can differ. For polygons with five or more sides, there exist equilateral pentagons, hexagons, and so on, which are not necessarily regular because their interior angles need not be equal.

Relation to other terms: A regular polygon is a special case of an equalsided polygon in which both all sides and all interior angles are equal. By contrast, an equalsided polygon can have unequal angles and hence does not have the full symmetry of a regular polygon. In some shapes, other properties such as diagonals or boundary angles play a crucial role in determining area and shape.

Properties and area: The area of an equalsided polygon is not determined by the side length alone; it depends on the specific arrangement of angles and diagonals. For special cases, formulas exist: the area of a regular polygon with n sides and side length s is known, and for a rhombus, area equals the product of its diagonals. Equilateral polygons with irregular angles illustrate the diversity within the class.