Table the Contents

What is a Polygon?

Polygons are several of the very first shapes we find out to attract as children, and they appear all approximately us. Polygons have the right to be regular or irregular. They deserve to be straightforward or complex, convex or concave. They can be the familiar shapes you see in geometry textbooks, or they can be strange shapes, like darts and bowties.

You are watching: Classify the polygon by the number of sides

The indigenous "polygon" method "many-angled," indigenous Greek. To be a polygon, a flat, closed shape should use just line segment to produce its sides. Therefore a one or any shape that has a curve is not a polygon.

The three identifying properties of any kind of polygon room that the polygon is:

A two-dimensional form Closing in a an are (having one interior and exterior) make with right sides

Types the Polygons

Let"s take a look in ~ the large array of shapes that are polygons and go right into detail.


A convex polygon has no inner angle higher than 180° (it has actually no inward-pointing sides). A concave polygon has actually one inner angle greater than 180°.A simple polygon encloses a single interior space (boundary) and does not have actually self-intersecting sides. Complicated polygons have self-intersecting sides!An irregular polygon walk not have actually congruent sides and also interior angles.A regular polygon has congruent sides and interior angles.


Regular and also Irregular Polygons

Regular polygons have congruent sides and interior angles. Every side is equal in length to every various other side, and every interior angle is same to all other interior angles. The variety of regular polygon is limitless.

Irregular polygons perform not have congruent sides and also angles. Residence plate top top a softball or baseball field is an irregular pentagon, since it has 5 sides through two 90° angles.


Convex and also Concave Polygons

A convex polygon close the door in an inner area without looking "dented." no one of its inner angles point inward. In geometry, you might have a four-sided polygon the points external in every directions, like a kite, or you could have the same four sides so two of them suggest inward, creating a dart. The kite is convex; the dart is concave.


Every inner angle the a convex polygon is much less than 180°. A concave polygon has at least one angle higher than 180°. Think the a bowtie-shaped simple hexagon (6 sides). It will have actually two inner angles better than 180°.


Simple and complicated Polygons

Simple polygons have actually no self-intersecting sides. Complex polygons, additionally called self-intersecting polygons, have actually sides that cross over each other. The classic star is a complicated polygon. Most world can doodle a star on record quickly, but few people brand it a pentagram, complex polygon, or self-intersecting polygon.


You cannot attract a facility triangle. For every polygon with 4 or much more sides, a complex polygon have the right to be drawn. A complicated quadrilateral is that acquainted bowtie shape, yet it is taken into consideration to have only 4 sides, because one pair of opposite sides has actually twisted to cross each other.

Just as you execute not count the crossed sides as four line segments, you execute not counting the two angles they produce as internal angles. The complicated quadrilateral still just has four sides and also four internal angles.


Complex polygons may be tough to imagine unless you think of them with elastic sides. If you can lift part of the polygon up and twist it, so two sides overcome one another, and then placed it down flat again, you would have actually a complicated polygon. Due to the fact that you twisted 2 sides, girlfriend still have actually those 2 sides (they carry out not twin in number by crossing). They likewise do not create brand-new vertices wherein they cross.


An unusual complex polygon is the antiparallelogram, i m sorry looks a little bit like bird wings. One antiparallelogram (or crossed parallelogram) has actually the normal 2 pairs that congruent, the opposite sides, yet one pair has been crossed, developing what appears to be two emotional triangles.


Like any parallelogram, though, the antiparallelogram still only has 4 sides and four internal angles. That diagonals, however, lie outside the shape!

Names the Polygons

Names the PolygonsPolygon ShapeNumber the Sides
Triangle3 sides
Square4 sides
Rectangle4 sides
Quadrilateral4 sides
Parallelogram4 sides
Rhombus4 sides
Dart4 sides
Kite4 sides
Pentagon5 sides
Hexagon6 sides
Heptagon7 sides
Octagon8 sides
Nonagon9 sides
Decagon10 sides
Dodecagon12 sides
Icosagon20 sides
Hectagon100 sides
n-gonn sides

Is it A Polygon?

The interiors of every polygons can be damaged up right into triangles, i m sorry is a handy way to find the sum of their inner angles. Take two much less than the variety of sides, n, and multiply times 180°: (n - 2) x 180°.


A circle is no a polygon, but a icosikaihenagon is a polygon. An icosikaihenagon is a 21-sided polygon. Many mathematicians and mathematics college student would merely write "21-gon" to surname it.

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Lesson Summary

Polygons have the right to be studied and classified in many different ways. You currently see that polygons can be continual or irregular, convex or concave, and simple or complex. When you check out an unfamiliar polygon, you deserve to determine that properties and classify that correctly.

To it is in a polygon, the shape must be flat, nearby in a space, and be make using only straight sides. Polygons through congruent sides and also angles space regular; every others room irregular. Polygons v all inner angles much less than 180° room convex; if a polygon has at least one internal angle higher than 180°, the is concave. Straightforward polygons do not cross their sides; complex polygons have self-intersecting sides. Polygons space all approximately you!

Next Lesson:

What is a continual Polygon?

What girlfriend learned:

After viewing the video, analysis these notes, and also studying the drawings, girlfriend will find out to:

Define a polygon acknowledge its identifying nature Distinguish between regular and irregular polygons, an easy and complex polygons, and concave and convex polygons Draw and also recognize examples of every the types of polygon