Perimeter of a Regular Polygon
P = n(l)
Where: P = perimeter
n = number of sides
l = length of each side
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A regular polygon is a shape that has n amount of sides, all being equal length, symmetrical to one another, and sharing a common central point (n ≥ 3 and must be a whole number.)
The perimeter of a regular polygon (as with any other shape with straight sides) is the number of all its sides added together. Therefore, since all of a regular polygon's sides are all the same size, you only need to multiply the number of its sides by their common length to get the shape's perimeter.
Regular Vs. Irregular
Irregular polygons are much more liberal shapes than regular polygons. Here's why:
- The sides of a regular polygon are all the same length (the shape is equilateral) where the sides of an irregular polygon can be all different lengths, all the same lengths, or any combination of the two. (Note: if the sides in an irregular polygon are all the same length, then the angles that form the shape must differ from each other.)
- Each side of a regular polygon must form the same angle with each of its adjacent sides (in other words, it must be equiangular.) The angles that the sides of an irregular polygon form can all be different, the same, or any combination of the two. (Note: if the angles in an irregular polygon are all the same, then the sides that form these angles must be different lengths.)
- Every angle and side of a regular polygon is the same distance from (in other words, is equidistant to) the center point of the shape.
About Polygons
It isn't a term used to refer to a lost parrot (Polly wanna be found?) A (simple) polygon is an enclosed figure consisting of three or more non-intersecting straight lines.
Name Origination
Poly- is a Greek term meaning "many" and -gon stems from the Greek term gonia, which means "angle."
If you're wondering where the names for polygons themselves originated, wonder no more. Their names are formed by using the Greek numbering system. However many sides the polygon has, its name starts with that number in Greek and is followed by the suffix -gon (the only exceptions are triangle and quadrilateral.)
So, for example, to name a polygon with 14 sides, find the term for the number fourteen in Greek and add –gon after it.
Here’s a list of the names of polygons based on how many sides they are made up of:
For polygons with more than twenty sides and less than one-hundred sides, a slightly different procedure is used. Use this graph to name polygons with this amount of sides:
Extra Facts
A polygon always has the same amount of angles that it has sides (and vise-versa.)
There are other kinds of polygons besides regular and irregular. There are simple polygons and complex ones. This help file focuses only on simple polygons.
Keep in mind that all sides of a polygon must be straight. There can't be any curved lines in a polygon.
Example
Find the perimeter of the regular polygon below.
P = n(l)
First, identify the number of sides the polygon has and the lengths of each of them:
Sides (n) = 4
Length for all sides (l) = 6 inches
(Since all of the sides of regular polygons are the same length, 6 is the length of all the sides of this one.)
Plug these values into the equation:
P = (4)(6)
Do the multiplication:
4(6) = 24
That gives us:
P = 24
which means that the perimeter of our polygon is 24 inches.
Helpful Definitions
Symmetrical: having each side share the same shape, size, and position of the other
Whole Number: a complete number which does not include a decimal, fraction, or a negative value.
Equilateral: having sides that are all the same length
Equiangular: having angles that are all the same size
Equidistant: being the same distance from/to
Related Websites:
http://www.mathsteacher.com.au/year7/ch09_polygons/05_polygon/pol.htm
http://mathworld.wolfram.com/RegularPolygon.html
Works Cited
Cahir, Donal. "Irregular Polygons." May 1999. Donal Cahir. 6 July 2006.
<http://www.ul.ie/~cahird/polyhedronmode/irregula.htm>.
Weisstein, Eric W. "Polygon." MathWorld. 17 June 2003. Wolfram Research, Inc.
6 July 2006.
<http://mathworld.wolfram.com/Polygon.html>.
Weisstein, Eric W. "Regular Polygon." MathWorld. 19 April 2006. Wolfram Research,
Inc. 6 July 2006. <http://mathworld.wolfram.com/RegularPolygon.html>.
"Polygon." Wikipedia. 4 July 2006. Wikimedia Foundation, Inc. 6 July 2006.
<http://en.wikipedia.org/wiki/Polygon>.
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