Polygons
A polygon is a plane shape with straight sides.
Is it a Polygon?
Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).
 |  |  |
| Polygon (straight sides) | Not a Polygon (has a curve) | Not a Polygon (open, not closed) |
Polygon comes from Greek. Poly- means "many" and -gon means "angle".
Types of Polygons
Regular or Irregular
If all angles are equal and all sides are equal, then it is regular, 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 pentagram) |
| Names of Polygons |
| If it is a Regular Polygon... | |||
| Name | Sides | Shape | Interior Angle |
|---|---|---|---|
| Triangle (or Trigon) | 3 |  | 60° |
| Quadrilateral (or Tetragon) | 4 |  | 90° |
| Pentagon | 5 |  | 108° |
| Hexagon | 6 |  | 120° |
| Heptagon (or Septagon) | 7 |  | 128.571° |
| Octagon | 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 | 179.64° | |
| Myriagon | 10,000 | 179.964° | |
| Megagon | 1,000,000 | ~180° | |
| Googolgon | 10100 | ~180° | |
| n-gon | n |  | (n-2) × 180° / n |
You can make names using this method:
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Example: a 62-sided polygon is a Hexacontadigon
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BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13-gon", "14-gon" ... "100-gon", etc.
Now, let's have some fun! Try to sing this song so you can memorize our lesson easily!
Before you leave this page, can you name a thing you usually use that resembles a polygon? Please leave your answer in a comment box.Thank you!
Hello everyone. You are all welcome to comment, suggest or add in such a way it will help my blog. thank you!
ReplyDeleteIt's really is amazing, we have many kinds of polygons.
ReplyDeleteyea, ma'm..actually, the world is made of polygons..:)
DeleteHeha ma'am, ang hirap namang i-memorize ang mga names ng polygon...
ReplyDeleteeto naman ung sakin, jeje
http://math260-simplemath.blogspot.com/
Yes Sir Albert..I can easily memotize until dodecagon, the rest, I should make an effort memorizing them!:)
DeleteEvery Christmas, teachers usually ask students to bring something that reminds Christmas and Christ' birth.My favorite thing to bring is "parol"..it represents pentagon polygon..how about yours?
ReplyDeleteThanks for the information mam. Now i know the name of polygons having 13 sides and above.
ReplyDeleteYou're welcome ma'm Cath..ngayon ko lang din yan nalaman :)
DeleteIn my case, we are using triangles or trigon as I knew now, in the age-grouping for the population which is in a pyramid or an inverted pyramid. And when at home, our roofs, doors, tables are examples of pyramid, am going out from the house in our tetragon gate, which will welcome me when am coming home...lol. pero true di ba....
ReplyDeleteYes ma'm Jocelyn..Polygon is very useful in stat huh? thank you for that info:)
Deletemam, how are we going to measure the exterior angles of a regular polygon?
ReplyDeleteExterior Angles of a Polygon Formula for sum of exterior angles:
DeleteThe sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°.
formula = 360/n
n is the number of sides
for example: Pentagon
n = 5 sides
360/5 = 72
This comment has been removed by the author.
ReplyDeletethank you po mam. mam how about finding the number of sides of a regular polygon when the sum of the measures of the vertex angle is given?
ReplyDeleteThe sum of the measures of the exterior angles of a polygon, one at each vertex, is always 360°.
Delete.
When you have a regular polygon, all the exterior angles have the same measure, as long as you measure corresponding angles at each vertex. So,
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[the angle measure in degrees] = [360 degrees] / [the number of vertices in the polygon]
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the number of vertices equals the number of sides, so
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[angle measure in degrees] = [360 degrees] / [the number of sides in the polygon]
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Let n be the number of sides.
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Then the angle measure is 360/n.
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Example:
PROBLEM 1:
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We know the angle measure is 30 degrees. We want to know the number of sides of the regular polygon.
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30 = 360/n
n = 360/30
n = 12
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The polygon has 12 sides.
"ma'am ang gnada ng BLOG mo..... talong talo ako hahahhaha.... my answer is SOCCER BALL"
ReplyDeleteSir, walang talo,lahat panalo kasi pinaghirapan natin ang mga gawa natin! If we combined our works, panalong panalo because it complements, OK?
Deletechecked!
ReplyDelete