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# Polygon Notes

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### Polygon Notes

1. 1. Polygons
2. 2. What is a Polygon???? Any ideas?
3. 3. A polygon is a closed plane figure with 3 or more sides (all straight lines, no curves).
4. 4. Classifying Polygons by # of Sides 3 sided Polygon = Triangle Hint: Think “Tri”cycle, “tri”pod, “Tri”lateration (Tri means 3)
6. 6. Classifying Polygons by # of Sides 5 sided Polygon = Pentagon Hint: Think “Pent”athalon, or the government building “The Pentagon”
7. 7. Classifying Polygons by # of Sides 6 sided Polygon = Hexagon Hint: Both “Hexagon” and “Six” have an ‘x’ in them
8. 8. Classifying Polygons by # of Sides 7 sided Polygon = Heptagon Hint: ???
9. 9. Classifying Polygons by # of Sides 8 sided Polygon = Octagon Hint: “oct”opus – 8 legs
10. 10. Classifying Polygons by # of Sides 9 sided Polygon = Nonagon Hint: “Non” is similar to “Nine”
11. 11. Classifying Polygons by # of Sides 10 sided Polygon = Decagon Hint: Think “Dec”ade (10 years
12. 12. Classifying Polygons by # of Sides 11 sided Polygon = Hendecagon Hint: ???
13. 13. Classifying Polygons by # of Sides 12 sided Polygon = Dodecagon Hint: ???
14. 14. Classifying Polygons by # of Sides Q: What do we call a polygon with more than 12 sides? A: An ‘n’-gon where ‘n’ is the number of sides Ex: a 20 sided polygon is a 20-gon
15. 15. Classifying Polygons by # of Sides # of Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Hendecagon 12 Dodecagon
16. 16. Classifications of Polygons Convex – all vertices point outward Concave – at least one vertex points inward towards the center of the polygon (The side looks like it “caved” in)
17. 17. Regular Polygons A Regular Polygon is a polygon in which all sides are the same length. Equilateral Triangle Square
18. 18. Review of Similar Triangles • 2 Triangles are similar if they have the same shape (i.e. the same angle in the same positions)
19. 19. Similar Polygons 2 polygons are similar if they have the same angles in the same positions (i.e. same shape) and the sides are proportional. Similar Pentagons Similar Trapezoids Similar Rectangles
20. 20. Sum of the Interior Angles of a Polygon The Sum of the Interior Angles of a Polygon can be found by the following expression: 180*(n – 2) Where n = number of sides n = 6; 180*(6-2) = 180*4 = 720° 140 ° +124 ° +92 ° +132 ° +141 ° = 629 ° 720 ° -629 ° = 91 °
21. 21. Apothem The apothem is a line segment from the center of a regular polygon (all sides congruent) to the midpoint of one of the sides. The apothem of a regular polygon forms a right angle with the side it connects with.
22. 22. Area of a Triangle (Review) The area of a triangle can be found by the following equation: A = ½*b*h
23. 23. Area of a Triangle (Review) A = ½*b*h; b=8, h=6 A = ½*8*6 A= ½*48 A= 24in 2
24. 24. Area of a Regular Polygon To find the area of a regular polygon, use the following formula: A = (1/2)*a*s*n a = apothem s = side length n = number of sides A = (1/2)*3*4*6 A = 36cm 2
25. 25. Exterior Angles of a Polygon The angle formed by any side of a polygon and the extension of its adjacent side. Exterior Angle
26. 26. Sum of the Exterior Angles of a Polygon The sum of the exterior angles of any polygon ALWAYS equals 360 ° 59 ° +78 ° +71 ° +75 °+ X = 360 ° 283° + X = 360 ° 360°-283° = 77° X = 77°