Polygon shapes names12/8/2023 This formula falls out of the fact that any simple polygon can be divided into n−2 triangles, each of which has interior angles that sum to 180 degrees (or pi radians). So, a square has interior angles that sum to 360 degrees ((4−2)×180), the interior angles of a hexagon sum to 720 degrees ((6−2)×180). For any simple polygon, the sum of its interior angles can be determined by the formula: Thus, every polygon has an equal number of vertices and angle. Credit: Texample CC-BY SA 2.5 Angles Of PolygonsĮvery polygon has an equal number of sides and vertices. The angles and sides of a square are all equal. For example, a square is a regular quadrilateral. An irregular polygon is one in which the sides and angles are unequal measures. A regular polygon is one in which all sides are equal length and all angles are of equal magnitude. Polygons are also classified according to their symmetries. The bowtie shape made form the square still has 4 interior angles and 4 vertices. In a self-intersecting polygon, the intersection of the lines does NOT create a new vertex or a new interior angle. For example, a rectangle would turn in to a bowtie-like shape. Imagine an elastic simple polygon that is picked up and twisted so that some of its sides cross each other. Self-intersecting polygons are sometimes called complex polygons. In contrast, a simple polygon has lines that do not intersect each other. Polygons are also differentiated as self-intersecting or simple. A self-intersecting polygon has at least one pair of lines that intersect. A concave polygon will always have at least one diagonal that falls outside of the area enclosed by the shape. In contrast, a concave polygon is any polygon that has at least one angle whose measure is greater than 180 degrees. This means that every diagonal of a convex polygon will fall inside the area enclosed by the shape. A convex polygon is any polygon whose interior angles are all less than 180 degrees. Polygons can be classified as convex or concave. This is because a circle is not made out of straight lines, it is a curve. What about a circle? Is a circle considered a polygon? The answer is no, a circle is not considered a polygon. Most polygons have a special name corresponding to the number of sides (quadrilateral-4 sides, pentagon-5 sides, hexagon, 6 sides, etc) or they can just be called an n-gon, where n corresponds to the number of sides (3-gon, 4-gon, 5-gon, etc). Therefore, the triangle is the absolute simplest possible polygon in Euclidean geometry. It takes at least 3 straight lines to enclose some area of space. According to Euclidean geometry, the smallest possible number of sides a polygon can have is 3. Most of the time, polygons are classified based on the number of their sides. Polygons can be classified in a number of ways relating to: Credit: Author Classification Of Polygons
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