We explain what polygons are and how these geometric figures are classified. Also, what are its characteristics and examples.
What are polygons?
A polygon is everything flat geometric figure that is composed of three or more straight lines that make up a closed figure. These consecutive lines are called sides and a polygon is also characterized by having three or more angles and vertices and being crossed by diagonals (with the exception of the triangle).
Although many geometric figures are polygons, not all are. Some examples of polygons are triangles, squares, rhombuses, rectangleshexagons, pentagons, among many others.
The word polygon comes from the Greek: polygons and derives from the word copwhich means many, and of gonos, which means sides. Each polygon is usually named according to the number of sides it has.
See also: Quadrilaterals
Characteristics of polygons
The main characteristics of polygons are:
- They are two-dimensional figures. Every polygon has two dimensions: height and width. Two-dimensional figures do not have the third dimension, which is depth, so polygons have neither volume nor weight.
- They are closed figures. To be considered a polygon, any polygon must be closed, that is, it must have angles and the figure must not be open. If one of the sides of a figure does not join another at one end, it is not a polygon.
- They are made up of segments or straight lines. The sides or lines of the polygon must be, without exception, straight. If any of the parts or sides of a geometric figure are curved, it is no longer a polygon.
Elements of a polygon
All polygons are characterized by having:
- Sides. These are the lines that form the figure. A polygon must have at least three sides and there is no maximum number of sides. A polygon can be, for example, a triangle (three-sided polygon), a pentagon (five-sided polygon), an octagon (eight-sided polygon), among many others.
- Vertices. They are the unions or intersections that occur when joining two sides or lines of the polygon. The number of vertices of a polygon is equal to the number of sides of the figure.
- Angles. They are the angles that are formed between two lines or sides of the polygon and that have a certain inclination or graduation.
- Exterior angles. They are the angles formed between one of the sides and a line outside the polygon.
- Diagonals. They are lines that can be joined within the polygon between one vertex and another non-consecutive vertex. The number of diagonals that can be drawn in a polygon will depend on the number of sides. The more sides a polygon has, the more diagonals can be drawn. The triangle is the only polygon that does not have diagonals.
Additionally, regular polygons have:
- Center. It is the point that is equidistant between all the sides and vertices of a regular polygon.
- Apothem. It is the distance between the center of the polygon and any of the sides.
- Central angleIt is the angle that has its vertex at the center of the polygon and its sides are formed by joining that center with two consecutive vertices of the polygon.
Types of polygons
Polygons can be classified according to certain criteria.
According to its shape:
- Simple polygon. It does not allow the crossing of its edges, that is, it forms a figure in which none of the sides intersect. It can be:
- convex polygon. Polygon in which at least one of its interior angles measures less than 180º.
- Concave polygon. Polygon in which at least one of its internal angles measures more than 180º.
- Complex polygon. Its edges (or sides) intersect. It is easily recognizable because one of the lines crosses another line of the polygon.
According to the relationship between its sides:
- Regular polygon. It has all sides and interior angles of the same length.
- irregular polygon. It has sides and interior angles of different lengths.
According to the number of sides:
Some examples are:
- Triangle (three-sided polygon).
- Quadrilateral (four-sided polygon).
- Pentagon (five-sided polygon).
- Hexagon (six-sided polygon).
- Heptagon (seven-sided polygon).
- Octagon (eight-sided polygon).
- Nonagon (nine-sided polygon).
- Decagon (ten-sided polygon).
- Pentadecagon (fifteen-sided polygon).
- Isodecagon (twenty-sided polygon).
- Triacontágon (polygon with thirty sides).
- Pentacontagon (polygon with fifty sides).
- Hectagone (one hundred sided polygon).
How do you calculate the perimeter and area of a polygon?
The perimeter of a polygon is the outline of the figure and is obtained by adding all its sidesIf it is a regular polygon (whose sides are the same length), multiplication can be performed. In the case of irregular polygons, multiplication is not possible because their sides do not have the same length and the sum must be performed directly.
To obtain the area of a polygon, the type of polygon you are working with must be taken into account, since The area is calculated differently according to each type of geometric figureThe formula will change depending on whether it is a triangle, a square, or any other regular or irregular polygon.
For example:
- Area of a rectangle = bxh (base times height).
- Area of a square = lxl (side by side).
- Area of a triangle = (bxh) 2 (base times height divided by two).
- Area of a rhombus = (D xd) 2 (major diagonal times minor diagonal divided by two).
In many cases, to find out the area of a given polygon you must decompose the figure into smaller figures, find out each of their areas, and then add them.
Polygons in everyday life
Polygons are geometric figures that are found both in nature and in human creations. Some examples are:
- In the starfish.
- In flowers and fruits.
- In the honeycombs.
- In the snow crystals.
- On traffic signs.
- In buildings such as houses and buildings.
- In objects such as books, pillows, soccer balls and boxes.
- In the pyramids.
- In furniture such as tables, benches and bookcases.
- On routes and paths.
- In clothing items such as scarves and t-shirts.
- On windows and doors.
- On the flags.
- In foods such as cakes, sandwiches, cheeses and cookies.
- In tools such as hammers and nuts.
- In appliances such as refrigerators and microwaves.
- On computers, cell phones and tablets.
- In sweets and chocolates.
- In sheets, curtains and towels.
- In swimming pools and flowerbeds.
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