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Polygons what is the difference between the perimeter and the area of a polygon

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The perimeter of a polygon is the length of its sides. The area is the space enclosed by the polygon.
The difference is similar to the difference between a fence around a yard and the space in the yard.

Posted on May 02, 2013

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Names of all polygons


Since there are an infinite number of polygons, I can't list all of their names. For the names of all polygons with up to 100 sides, see http://en.wikipedia.org/wiki/Polygon

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If the ratio of the corresponding side lengths of two similar polygons is 5:9, what is the ratio of their perimeters?


This works for any polygon:

Say you have 2 squares - the sides are 5 and 9
Perimeter 1 = 20
Perimeter 2 = 36

20:36 = 5:9

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All shapes of polygons


There are an infinite number of shapes of polygons --- too many to list here. See http://en.wikipedia.org/wiki/Polygon

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All shapes of polygons


There are an infinite number of polygons, from triangles with three sides, quadrilaterals with four sides, and going on from there.

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What is a polygon with 15 diagonals


For convex polygons there is a relation linking the number of sides to the number of diagonals. Here it is, with n=number of sides
number of diagonals=n*(n-3)/2. Obviously the number of sides must be greater or equal to 3.
If you use the relation for a hexagon (n=6) the number of diagonals is 9. With n=7, the number of diagonals is 14, and for n=8 the number of diagonals is 8*(8-3)/2=20. The answer is that there does not exist a CONVEX polygon with 15 diagonals.
You can also try to solve the quadratic equation n(n-3)/2=15 for a positive integer. And you will not find a solution.
For polygons that are not convex there may be many solutions or no solutions. I leave that to you as an exercise.

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How do convex polygons differ from non-convex polygons?


A convex polygon is one with each of its interior angles less than 180 degrees and every line segment between any of its two vertices remains inside or on the boundary of the polygon.

150px-pentagon.svg.pngExample of a convex polygon (WIKIPEDIA)


A concave polygon will always possess an interior angle with a measure that is greater than 180 degrees.

150px-simple_polygon.svg.pngExample of a concave polygon (WIKIPEDIA)

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Regular polygons


not the question of this site.

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