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  2. Pentagon - Wikipedia

    en.wikipedia.org/wiki/Pentagon

    In geometry, a pentagon (from Greek πέντε (pente) 'five' and γωνία (gonia) 'angle' [1]) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon (or star pentagon) is called a pentagram.

  3. List of polygons - Wikipedia

    en.wikipedia.org/wiki/List_of_polygons

    A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain. These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular ...

  4. Equilateral pentagon - Wikipedia

    en.wikipedia.org/wiki/Equilateral_pentagon

    In geometry, an equilateral pentagon is a polygon in the Euclidean plane with five sides of equal length. Its five vertex angles can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the regular pentagon is unique, because it is equilateral and moreover it is equiangular (its five angles are equal ...

  5. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    The area A of a convex regular n-sided polygon having side s, ... The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, ...

  6. Polygon - Wikipedia

    en.wikipedia.org/wiki/Polygon

    For any two simple polygons of equal area, the Bolyai–Gerwien theorem asserts that the first can be cut into polygonal pieces which can be reassembled to form the second polygon. The lengths of the sides of a polygon do not in general determine its area. [9] However, if the polygon is simple and cyclic then the sides do determine the area. [10]

  7. Constructible polygon - Wikipedia

    en.wikipedia.org/wiki/Constructible_polygon

    The five known Fermat primes are: F 0 = 3, F 1 = 5, F 2 = 17, F 3 = 257, and F 4 = 65537 (sequence A019434 in the OEIS). Since there are 31 nonempty subsets of the five known Fermat primes, there are 31 known constructible polygons with an odd number of sides. The next twenty-eight Fermat numbers, F 5 through F 32, are known to be composite. [3]

  8. Shoelace formula - Wikipedia

    en.wikipedia.org/wiki/Shoelace_formula

    Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]

  9. Star polygon - Wikipedia

    en.wikipedia.org/wiki/Star_polygon

    Regular star polygons can be created by connecting one vertex of a regular p-sided simple polygon to another vertex, non-adjacent to the first one, and continuing the process until the original vertex is reached again. [5]