Polygons
What is a Polygon????
Any ideas?
A polygon is a closed plane figure with 3 or more sides (all straight lines, no curves).
Classifying Polygons by # of Sides
3 sided Polygon =
Triangle
Hint: Think “Tri”cycle, “tri”pod, “Tri”lateration (Tri means 3)
Classifying Polygons by # of Sides
4 sided Polygon =
Quadrilateral
Hint: Think “Quad”rant, “Quad”ruple, “Quad” (AKA 4-Wheeler)
Classifying Polygons by # of Sides
5 sided Polygon =
Pentagon
Hint: Think “Pent”athalon, or the government building “The Pentagon”
Classifying Polygons by # of Sides
6 sided Polygon =
Hexagon
Hint: Both “Hexagon” and “Six” have an ‘x’ in them
Classifying Polygons by # of Sides
7 sided Polygon =
Heptagon
Hint: ???
Classifying Polygons by # of Sides
8 sided Polygon =
Octagon
Hint: “oct”opus – 8 legs
Classifying Polygons by # of Sides
9 sided Polygon =
Nonagon
Hint: “Non” is similar to “Nine”
Classifying Polygons by # of Sides
10 sided Polygon =
Decagon
Hint: Think “Dec”ade (10 years
Classifying Polygons by # of Sides
11 sided Polygon =
Hendecagon
Hint: ???
Classifying Polygons by # of Sides
12 sided Polygon =
Dodecagon
Hint: ???
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
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
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)
Regular Polygons
A Regular Polygon is a polygon in which all sides are the same length.
Equilateral Triangle Square
Review of Similar Triangles
• 2 Triangles are similar if they have the same shape (i.e. the same angle in the same positions)
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
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°
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.
Area of a Triangle (Review)
The area of a triangle can be found by the following equation:
A = ½*b*h
Area of a Triangle (Review)
A = ½*b*h; b=8, h=6A = ½*8*6A= ½*48A= 24in2
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 = 36cm2
Exterior Angles of a Polygon
The angle formed by any side of a polygon and the extension of its adjacent side.
Exterior Angle
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°