Difference between revisions of "Polygon"
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# Higher orders of polygons are: [[nonagon]] (9-sided), [[decagon]] (10-sided), [[unodecagon]] (11-sided), [[duodecagon]] (12-sided) etc. | # Higher orders of polygons are: [[nonagon]] (9-sided), [[decagon]] (10-sided), [[unodecagon]] (11-sided), [[duodecagon]] (12-sided) etc. | ||
# Polygons of higher orders than the duodecagon are often named ''n''-gons, where ''n'' is the amount of its sides. For example, a 42-gon would be a polygon with 42 sides. | # Polygons of higher orders than the duodecagon are often named ''n''-gons, where ''n'' is the amount of its sides. For example, a 42-gon would be a polygon with 42 sides. | ||
| − | + | ==Formulas== | |
| − | + | The [[perimeter]] of a regular polygon is equal to <math>n sin\frac{180}{n} (2) (r)</math>, where ''r'' equals the length of the radius.<br> | |
| + | The [[area]] of a regular polygon is equal to <math>n sin\frac{180}{n}cos\frac{180}{n}(r^2)</math> | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 16:52, May 20, 2007
A polygon is a union of disjoint line segments that is path-connected.
A Regular polygon has all sides equal and all angles equal.
Types, by number of sides.
- There is no such mathematical entity as a one sided polygon in a plane. (For higher dimensional analogies, see Mobius strip and Klein bottle.)
- As with the one-sided polygon, there is no such thing as a two-sided polygon. (This would be two overlapping line segments.)
- Triangle - three sided, see isosceles triangle, equilateral triangle, right triangle
- Quadrilateral - four sided, see also square, rectangle, rhombus, and trapezoid
- Pentagon - five sided. The most famous one houses the Department of Defense.
- Hexagon - six sided, the shape of a bee hive cell, also used in some board games
- Heptagon - seven sided. Some coins have been been heptagonal.
- Octagon - eight sided, used for stop signs in the U.S.
- Higher orders of polygons are: nonagon (9-sided), decagon (10-sided), unodecagon (11-sided), duodecagon (12-sided) etc.
- Polygons of higher orders than the duodecagon are often named n-gons, where n is the amount of its sides. For example, a 42-gon would be a polygon with 42 sides.
Formulas
The perimeter of a regular polygon is equal to 
, where r equals the length of the radius.
The area of a regular polygon is equal to 
