Regular Polygons

[Louis Zampini]

Regular Polygons

• A polygon is a closed figure with straight edges.
• Examples: P152 1b is a polygon. 1a and 1c are not. 1a is not closed because it has an edge sticking out. 1c has two curved edges.
• A regular polygon is a polygon in which all the sides are the same length and all the interior angles are the same degree. These polygons have names.
• Examples: Triangle, square, pentagon, hexagon, heptagon, octagon, decagon, dodecagon, and so on. For a more complete list, you can check out the polygon page on wikipedia http://en.wikipedia.org/wiki/Polygon. You are only required to know the ones mentioned above.
  

Concave/Convex

• A concave figure is classified as concave if when the edges are extended, at least one edge crosses one of the polygon's edges.
• Examples: P152 2b and 2c are concave. Take a ruler and place it on those polygons' edges. Extend the lines with your pencil. Watch how in 2b line GH crosses near J. Line HI crosses near K. Similarly in 2c, line AF crosses near D and line EF crosses near B.
• A convex figure is classified as convex if when the edges are extended, none cross any of the polygon's edges.
• Examples: P152 2a is convex. Take a ruler and place it on those polygons' edges. Extend the lines with your pencil. None of the lines you drew cross the polygon's edges.

Diagonals

•  A diagonal in a polygon is a line drawn from one corner to another corner, not including the polygon's edges.
• Example: http://math.com/school/subject3/images/S3U2L1DP3.gif
• To calculate how many diagonals there are in any given polygon, use the following formula: n ( n - 3 ) / 2
• n = number of sides. This formula requires you to take n minus 3, multiplied by n, divided by 2.
• Examples: P153 5a. 7 sides, how many diagonals? 7 minus 3 equals 4. 4 times 7 equals 28. 28 divided by 2 equals 14. In a seven sided polygon, you can draw 14 diagonals.

Interior Angles

• In any polygon, the total number of interior angles can be found using the following formula: ( n - 2 ) x 180
  
• n = number of sides. This formula requires you to take n minus 2, multiplied by 180.
• Examples: P153 7a. 4 sides, what is the sum of the interior angles? 4 minus 2 equals 2. 2 times 180 equals 360. There are 360° in a 4 sided polygon.
• In a regular polygon, each interior angle is the same measure. To find this measure, you can use the following formula: ( n - 2 ) x 180 / n
• n - number of sides. This formula requires you to take n minus 2, multiplied by 180, divided by n.
• Examples: P155 3a. 5 sides, what is the measure of the interior angles in this polygon? 5 minus 2 equals 5. 3 times 180 equals 540. 540 divided by 5 equals 108. Each interior angle in a pentagon is 108°.

Perimeter

• In any regular polygon, the perimeter can be found by multiplying the number of sides by the side length, using the following formula: P = S x N
  
• p = perimeter. s = side length. n = number of sides . This formula requires you to multiply s by n.
• Examples: P157 1. A pentagon with a side length of 4.3. A pentagon has 5 sides. 4.3 times 5 equals 21.5.

[LOUiS]

The previous post is information for a grade 8 class doing polygons.
The pages reference the carrousel workbook.