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°