Polygons

Types Of Polygon Before we start learning about types of polygon, let us first learn the definition of a polygon. A polygon is a closed shape figure that has a minimum of three sides and three vertices. The term ‘poly’ means ‘many’ and ‘gon’ means ‘angle’. Thus, polygons have many angles. The perimeter and The classification of polygons is described based on the numbers of sides and vertices. For example, a polygon as four sides and four angles, then it is quadrilateral. The polygons up to 12 sides are the important ones. We are going to learn here polygon’s types based on the number of sides of the closed figure along with examples and diagrams. Also, read: • • • • All the polygon from triangle to decagon are given here in the below figures, respectively. These are the basic types of regular polygons which we see in our daily life. Also, these polygons have certain properties based on their area, perimeter, diagonals, etc. Classification of Polygons and their Properties A two-dimensional shape which is enclosed by a finite number of straight lines joining in the form of a closed-loop is called a polygon. The line segments which make the polygon are known as polygon’s sides or edges. Whereas the corner or the point where any two sides join is called the vertex of the polygon. Now, based on the number of sides and angles, polygons are classified into different types, which we are going to discuss here. Polygons are classified into various types based on the number of sides ...

Polygon Formula Before starting with the polygon formula, let us recall the definition of apolygon. A polygon is a closed 2-D shapethat has three or more straight lines.A polygon should have at least three sides. Each side of the line segment intersects with another line segment at the vertex. Let us learn more about the different polygons and their formulas. Types of Polygon Based on the angle measure and the sides of a • Regular Polygon – All the interior angles and the sides are of the same measure • Irregular Polygon – All the interior angles and the sides have different values • • Concave Polygon – Polygons that have one or more interior angles with a measure of>180 degrees The number of sides of a polygon determines its shape and it's named after its number of sides.Common examples of polygons aretriangles, squares, pentagons, hexagons, etc. Below are the listed polygons based on their number of sides. What is Polygon Formula? The important formulas associated with a regular polygon aregiven below: Formula 1:For a regular 'n' sided polygon,the sum of Formula 2: The number of diagonals of an “n-sided” polygon =[n(n-3)]/2 Formula 3:The measure of each interior angle of a regular n-sided polygon = [(n-2)180°]/n Formula 4:The measure of exterior angles of a regular n-sided polygon = 360°/n Formula 5: Formula 6:In terms of the Properties of Polygon The important properties of the polygon are • The sum of the interior angles of all the quadrangles = 360°. • If at least one...

home / geometry / shape / polygon Polygon A polygon is a closed The line segments that form a polygon are called sides. Two connected sides form an angle at a point called a vertex. A diagonal is a line segment joining two non-consecutive vertices. In the polygon below, AB, BC, CD, and AD are four sides. They form four angles: ∠A, ∠B, ∠C, and ∠D. AC and BD are two diagonals. There are many ways to classify polygons; the following are some of them. Regular and irregular polygons Regular polygon A regular polygon is a polygon in which all sides have equal length (equilateral) and all angles have equal measure (equiangular). Below are some examples. Irregular polygon An irregular polygon has sides or angles that are not congruent, as shown below. Convex and concave polygons Polygons can be classified as either convex or concave. Convex polygon If all the interior angles of a polygon are less than 180°, it is convex. A regular polygon is always convex. The following are a few examples. Concave polygon If one or more interior angles of a polygon are larger than 180°, it is concave. A concave polygon is always an irregular polygon. The following are a few examples. The interior angles larger than 180° are marked with a red arc. Classifying polygons by their number of sides Polygons are commonly classified based on the number of sides they have. In general, a polygon with n-number of sides is called an n-gon. Some important polygons have specific names, such as triangles, pentago...

Example: What are the interior and exterior angles of a regular hexagon? A regular hexagon has 6 sides, so: Exterior Angle = 360 °/ 6 = 60° Interior Angle = 180 °− 60° = 120° And now for some names: "Circumcircle, Incircle, Radius and Apothem ..." Sounds quite musical if you repeat it a few times, but they are just the names of the "outer" and "inner" circles (and each radius) that can be drawn on a polygon like this: The "outside" circle is called a circumcircle, and it connects all vertices (corner points) of the polygon. The radius of the circumcircle is also the radius of the polygon. The "inside" circle is called an incircle and it just touches each side of the polygon at its midpoint. The radius of the incircle is the apothem of the polygon. (Not all polygons have those properties, but triangles and regular polygons do). Breaking into Triangles We can learn a lot about regular polygons by breaking them into triangles like this: Notice that: • the "base" of the triangle is one side of the polygon. • the "height" of the triangle is the "Apothem" of the polygon Now, the Area of one triangle = base × height / 2 = side × apothem / 2 To get the area of the whole polygon, just add up the areas of all the little triangles ("n" of them): Area of Polygon = n× side × apothem / 2 And since the perimeter is all the sides = n × side, we get: Area of Polygon = perimeter × apothem / 2 A Smaller Triangle By cutting the triangle in half we get this: (Note: The angles are in The small ...

Recent Examples on the Web Extra contacts on the whole body, for instance including the knees and elbows, enable the robot to increase its agility and robustness by enhancing the support polygon. — Evan Ackerman, IEEE Spectrum, 31 Aug. 2018 CuLitho produces otherwise hard-to-calculate curvy polygons on the mask, which results in a greater depth of focus for the pattern cast onto the wafer. — IEEE Spectrum, 23 Mar. 2023 Either way, the result in terms of the game’s implementation is an obvious and clear collaboration, with the team at FromSoftware struggling to make do with the original PlayStation’s polygon limits while trying to realize Kawamori’s mecha designs. — Ollie Barder, Forbes, 9 Mar. 2023 And the show suggests that when Camilla was beginning her relationship with the Prince of Wales, her on-again-off-again boyfriend Parker Bowles was sleeping with Princess Anne, creating not a love triangle, but some sort of love polygon, involving the Queen's two oldest children. — Caroline Hallemann, Town & Country, 2 Nov. 2022 Your house is in a tornado polygon. — Howard Koplowitz | [email protected], al, 13 Dec. 2021 Low- polygon models, blurry textures, and low-resolution effects are replaced with shiny new upgrade in Portal with RTX. — Andrew Cunningham, Ars Technica, 29 Nov. 2022 With ray tracing, the skeletal rig can be rendered as a simple small- polygon figure or in a more complex human form. — Discover Magazine, 29 June 2010 The tattoo, only a few inches long, is a spa...

Polygon comes from Greek. Poly- means "many" and -gon means "angle". Types of Polygons Regular or Irregular A regular polygon has all angles equal and all sides equal, otherwise it is irregular Regular Irregular Concave or Convex A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°. If any internal angle is greater than 180° then the polygon is concave. ( Think: concave has a "cave" in it) Convex Concave Simple or Complex A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Many rules about polygons don't work when it is complex. Simple Polygon (this one's a Pentagon) Complex Polygon (also a Pentagon) More Examples Irregular Hexagon Concave Octagon Complex Polygon (a "star polygon", in this case a Play With Them! Try Names of Polygons If it is a Regular Polygon... Name Sides Shape Interior Angle (or Trigon) 3 60° (or Tetragon) 4 90° 5 108° 6 120° Heptagon (or Septagon) 7 128.571° 8 135° Nonagon (or Enneagon) 9 140° Decagon 10 144° Hendecagon (or Undecagon) 11 147.273° Dodecagon 12 150° Triskaidecagon 13 152.308° Tetrakaidecagon 14 154.286° Pentadecagon 15 156° Hexakaidecagon 16 157.5° Heptadecagon 17 158.824° Octakaidecagon 18 160° Enneadecagon 19 161.053° Icosagon 20 162° Triacontagon 30 168° Tetracontagon 40 171° Pentacontagon 50 172.8° Hexacontagon 60 174° Heptacontagon 70 174.857° Octacontagon 80 175.5° Enneacontagon 90 176° Hectagon 100 176.4° Chiliagon 1,000 ...

The word "polygon" means "many-angled," from Greek. To be a polygon, a flat, closed shape must use only line segments to create its sides. So a circle or any shape that has a curve is not a polygon. The three identifying properties of any polygon are that the polygon is: • A two-dimensional shape • Closing in a space (having an interior and exterior) • Made with straight sides Types of polygons Let's take a look at the vast array of shapes that are polygons and go into detail. Types of Polygons • A convex polygon has no interior angle greater than 180° (it has no inward-pointing sides). A concave polygon has one interior angle greater than 180°. • A simple polygon encloses a single interior space (boundary) and does not have self-intersecting sides. Complex polygons have self-intersecting sides! • An irregular polygon does not have congruent sides and interior angles. • A regular polygon has congruent sides and interior angles. Various polygons Regular and irregular polygons Irregular polygons do not have congruent sides and angles. Home plate on a softball or baseball field is an irregular pentagon, because it has five sides with two 90° angles. Regular And Irregular Polygons Convex and concave polygons A convex polygon closes in an interior area without looking "dented." None of its interior angles point inward. In geometry, you could have a four-sided polygon that points outward in all directions, like a kite, or you could have the same four sides so two of them point i...