Section 1-6 
Two-Dimensional Figures 
Monday, September 22, 14
Essential Questions 
• How do you identify and name polygons? 
• How do you find perimeter, circumference, 
and area of tw...
Vocabulary 
1. Polygon: 
2. Vertex of a Polygon: 
3. Concave: 
4. Convex: 
5. n-gon: 
6. Equilateral Polygon: 
Monday, Sep...
Vocabulary 
1. Pol y g o n : A closed figure whose sides are all line 
segments 
2. Vertex of a Polygon: 
3. Concave: 
4. ...
Vocabulary 
1. Pol y g o n : A closed figure whose sides are all line 
segments 
2. Ver t e x o f a P o l y g o n : The po...
Vocabulary 
1. Pol y g o n : A closed figure whose sides are all line 
segments 
2. Ver t e x o f a P o l y g o n : The po...
Vocabulary 
1. Pol y g o n : A closed figure whose sides are all line 
segments 
2. Ver t e x o f a P o l y g o n : The po...
Vocabulary 
1. Pol y g o n : A closed figure whose sides are all line 
segments 
2. Ver t e x o f a P o l y g o n : The po...
Vocabulary 
1. Pol y g o n : A closed figure whose sides are all line 
segments 
2. Ver t e x o f a P o l y g o n : The po...
Vocabulary 
7. Equiangular Polygon: 
8. Regular Polygon: 
9. Perimeter: 
10. Circumference: 
11. Area: 
Monday, September ...
Vocabulary 
7. Equ i a n g u l a r P o l y g o n : A polygon where all angles 
are congruent 
8. Regular Polygon: 
9. Peri...
Vocabulary 
7. Equ i a n g u l a r P o l y g o n : A polygon where all angles 
are congruent 
8. Reg u la r P o l y g o n ...
Vocabulary 
7. Equ i a n g u l a r P o l y g o n : A polygon where all angles 
are congruent 
8. Reg u la r P o l y g o n ...
Vocabulary 
7. Equ i a n g u l a r P o l y g o n : A polygon where all angles 
are congruent 
8. Reg u la r P o l y g o n ...
Vocabulary 
7. Equ i a n g u l a r P o l y g o n : A polygon where all angles 
are congruent 
8. Reg u la r P o l y g o n ...
Vocabulary 
7. Equ i a n g u l a r P o l y g o n : A polygon where all angles 
are congruent 
8. Reg u la r P o l y g o n ...
Area Formulas 
Where are some places that you find these formulas? 
Monday, September 22, 14
Example 1 
Make four drawings (using a straight edge) so 
that two of your drawings are polygons and 
two are not. Label w...
Example 1 
Make four drawings (using a straight edge) so 
that two of your drawings are polygons and 
two are not. Label w...
Example 1 
Make four drawings (using a straight edge) so 
that two of your drawings are polygons and 
two are not. Label w...
Example 1 
Make four drawings (using a straight edge) so 
that two of your drawings are polygons and 
two are not. Label w...
Example 1 
Make four drawings (using a straight edge) so 
that two of your drawings are polygons and 
two are not. Label w...
Polygon Names 
3 sides: 4 sides: 5 sides: 
6 sides: 7 sides: 8 sides: 
Monday, September 22, 14
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle 
6 sides: 7 sides: 8 sides: 
Monday, September 22, 14
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle 
6 sides: 7 sides: 8 sides: 
Monday, September 22, 14
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral 
6 sides: 7 sides: 8 sides: 
Monday, September 22, 14
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral 
6 sides: 7 sides: 8 sides: 
Monday, September 22, 14
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral Pentagon 
6 sides: 7 sides: 8 sides: 
Monday, September ...
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral Pentagon 
6 sides: 7 sides: 8 sides: 
Monday, September ...
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral Pentagon 
6 sides: 7 sides: 8 sides: 
Hexagon 
Monday, S...
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral Pentagon 
6 sides: 7 sides: 8 sides: 
Hexagon 
Monday, S...
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral Pentagon 
6 sides: 7 sides: 8 sides: 
Hexagon Heptagon 
...
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral Pentagon 
6 sides: 7 sides: 8 sides: 
Hexagon Heptagon 
...
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral Pentagon 
6 sides: 7 sides: 8 sides: 
Hexagon Heptagon O...
Polygon Names 
3 sides: 4 sides: 5 sides: 
Triangle Quadrilateral Pentagon 
6 sides: 7 sides: 8 sides: 
Hexagon Heptagon O...
Polygon Names 
9 sides: 10 sides: 12 sides: 
Monday, September 22, 14
Polygon Names 
9 sides: 10 sides: 12 sides: 
Nonagon 
Monday, September 22, 14
Polygon Names 
9 sides: 10 sides: 12 sides: 
Nonagon 
Monday, September 22, 14
Polygon Names 
9 sides: 10 sides: 12 sides: 
Nonagon Decagon 
Monday, September 22, 14
Polygon Names 
9 sides: 10 sides: 12 sides: 
Nonagon Decagon 
Monday, September 22, 14
Polygon Names 
9 sides: 10 sides: 12 sides: 
Nonagon Decagon Dodecagon 
Monday, September 22, 14
Polygon Names 
9 sides: 10 sides: 12 sides: 
Nonagon Decagon Dodecagon 
Monday, September 22, 14
Example 2 
Draw a concave hexagon. Then draw a convex octagon. 
Monday, September 22, 14
Example 2 
Draw a concave hexagon. Then draw a convex octagon. 
Monday, September 22, 14
Example 2 
Draw a concave hexagon. Then draw a convex octagon. 
Monday, September 22, 14
Example 2 
Draw a concave hexagon. Then draw a convex octagon. 
Monday, September 22, 14
Example 2 
Draw a concave hexagon. Then draw a convex octagon. 
Monday, September 22, 14
Example 3 
Draw a regular quadrilateral. 
Monday, September 22, 14
Example 3 
Draw a regular quadrilateral. 
Monday, September 22, 14
Example 4 
Identify the figure based on the number of 
sides. Is it concave or convex? Is it equilateral, 
equiangular, or...
Example 4 
Identify the figure based on the number of 
sides. Is it concave or convex? Is it equilateral, 
equiangular, or...
Example 4 
Identify the figure based on the number of 
sides. Is it concave or convex? Is it equilateral, 
equiangular, or...
Example 4 
Identify the figure based on the number of 
sides. Is it concave or convex? Is it equilateral, 
equiangular, or...
Example 5 
Find the perimeter of a rectangle whose length 
is 8.3 cm and width is 3.2 cm. 
Monday, September 22, 14
Example 5 
Find the perimeter of a rectangle whose length 
is 8.3 cm and width is 3.2 cm. 
Monday, September 22, 14
Example 5 
Find the perimeter of a rectangle whose length 
is 8.3 cm and width is 3.2 cm. 
8.3 cm 
Monday, September 22, 1...
Example 5 
Find the perimeter of a rectangle whose length 
is 8.3 cm and width is 3.2 cm. 
8.3 cm 
3.2 cm 
Monday, Septemb...
Example 5 
Find the perimeter of a rectangle whose length 
is 8.3 cm and width is 3.2 cm. 
8.3 cm 
3.2 cm 
P = 2l + 2w 
Mo...
Example 5 
Find the perimeter of a rectangle whose length 
is 8.3 cm and width is 3.2 cm. 
8.3 cm 
3.2 cm 
P = 2l + 2w 
= ...
Example 5 
Find the perimeter of a rectangle whose length 
is 8.3 cm and width is 3.2 cm. 
8.3 cm 
3.2 cm 
P = 2l + 2w 
= ...
Example 5 
Find the perimeter of a rectangle whose length 
is 8.3 cm and width is 3.2 cm. 
8.3 cm 
3.2 cm 
P = 2l + 2w 
= ...
Example 5 
Find the perimeter of a rectangle whose length 
is 8.3 cm and width is 3.2 cm. 
8.3 cm 
3.2 cm 
P = 2l + 2w 
= ...
Example 6 
Find the circumference of a circle with a 
diameter of 14 in. 
Monday, September 22, 14
Example 6 
Find the circumference of a circle with a 
diameter of 14 in. 
Monday, September 22, 14
Example 6 
Find the circumference of a circle with a 
diameter of 14 in. 
14 in. 
Monday, September 22, 14
Example 6 
Find the circumference of a circle with a 
diameter of 14 in. 
14 in. C = 2π r = π d 
Monday, September 22, 14
Example 6 
Find the circumference of a circle with a 
diameter of 14 in. 
14 in. C = 2π r = π d 
C = π d 
Monday, Septembe...
Example 6 
Find the circumference of a circle with a 
diameter of 14 in. 
14 in. C = 2π r = π d 
C = π d 
C = π (14) 
Mond...
Example 6 
Find the circumference of a circle with a 
diameter of 14 in. 
14 in. C = 2π r = π d 
C = π d 
C = π (14) 
C ≈ ...
Problem Set 
Monday, September 22, 14
Problem Set 
p. 61 #1-27 odd, 44-47 
“Nobody got anywhere in the world by simply being 
content.” - Louis L’Amour 
Monday,...
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Geometry Section 1-6 1112

  1. 1. Section 1-6 Two-Dimensional Figures Monday, September 22, 14
  2. 2. Essential Questions • How do you identify and name polygons? • How do you find perimeter, circumference, and area of two-dimensional figures? Monday, September 22, 14
  3. 3. Vocabulary 1. Polygon: 2. Vertex of a Polygon: 3. Concave: 4. Convex: 5. n-gon: 6. Equilateral Polygon: Monday, September 22, 14
  4. 4. Vocabulary 1. Pol y g o n : A closed figure whose sides are all line segments 2. Vertex of a Polygon: 3. Concave: 4. Convex: 5. n-gon: 6. Equilateral Polygon: Monday, September 22, 14
  5. 5. Vocabulary 1. Pol y g o n : A closed figure whose sides are all line segments 2. Ver t e x o f a P o l y g o n : The point where two sides of a polygon meet 3. Concave: 4. Convex: 5. n-gon: 6. Equilateral Polygon: Monday, September 22, 14
  6. 6. Vocabulary 1. Pol y g o n : A closed figure whose sides are all line segments 2. Ver t e x o f a P o l y g o n : The point where two sides of a polygon meet 3. Concave: A polygon that has an indentation 4. Convex: 5. n-gon: 6. Equilateral Polygon: Monday, September 22, 14
  7. 7. Vocabulary 1. Pol y g o n : A closed figure whose sides are all line segments 2. Ver t e x o f a P o l y g o n : The point where two sides of a polygon meet 3. Concave: A polygon that has an indentation 4. Convex: A polygon that has no indentations 5. n-gon: 6. Equilateral Polygon: Monday, September 22, 14
  8. 8. Vocabulary 1. Pol y g o n : A closed figure whose sides are all line segments 2. Ver t e x o f a P o l y g o n : The point where two sides of a polygon meet 3. Concave: A polygon that has an indentation 4. Convex: A polygon that has no indentations 5. n-gon: A polygon that has n sides 6. Equilateral Polygon: Monday, September 22, 14
  9. 9. Vocabulary 1. Pol y g o n : A closed figure whose sides are all line segments 2. Ver t e x o f a P o l y g o n : The point where two sides of a polygon meet 3. Concave: A polygon that has an indentation 4. Convex: A polygon that has no indentations 5. n-gon: A polygon that has n sides 6. Equ i la t e r a l P o l y g o n : A polygon where all sides are congruent Monday, September 22, 14
  10. 10. Vocabulary 7. Equiangular Polygon: 8. Regular Polygon: 9. Perimeter: 10. Circumference: 11. Area: Monday, September 22, 14
  11. 11. Vocabulary 7. Equ i a n g u l a r P o l y g o n : A polygon where all angles are congruent 8. Regular Polygon: 9. Perimeter: 10. Circumference: 11. Area: Monday, September 22, 14
  12. 12. Vocabulary 7. Equ i a n g u l a r P o l y g o n : A polygon where all angles are congruent 8. Reg u la r P o l y g o n : A polygon where all sides are congruent and all angles are congruent 9. Perimeter: 10. Circumference: 11. Area: Monday, September 22, 14
  13. 13. Vocabulary 7. Equ i a n g u l a r P o l y g o n : A polygon where all angles are congruent 8. Reg u la r P o l y g o n : A polygon where all sides are congruent and all angles are congruent 9. Per i m e t e r : The sum of the lengths of the sides of a polygon; The distance around a polygon 10. Circumference: 11. Area: Monday, September 22, 14
  14. 14. Vocabulary 7. Equ i a n g u l a r P o l y g o n : A polygon where all angles are congruent 8. Reg u la r P o l y g o n : A polygon where all sides are congruent and all angles are congruent 9. Per i m e t e r : The sum of the lengths of the sides of a polygon; The distance around a polygon 10. Circumference: The distance around a circle 11. Area: Monday, September 22, 14
  15. 15. Vocabulary 7. Equ i a n g u l a r P o l y g o n : A polygon where all angles are congruent 8. Reg u la r P o l y g o n : A polygon where all sides are congruent and all angles are congruent 9. Per i m e t e r : The sum of the lengths of the sides of a polygon; The distance around a polygon 10. Circumference: The distance around a circle C = 2π r = π d 11. Area: Monday, September 22, 14
  16. 16. Vocabulary 7. Equ i a n g u l a r P o l y g o n : A polygon where all angles are congruent 8. Reg u la r P o l y g o n : A polygon where all sides are congruent and all angles are congruent 9. Per i m e t e r : The sum of the lengths of the sides of a polygon; The distance around a polygon 10. Circumference: The distance around a circle C = 2π r = π d 11. Area: The space in square units a figure covers Monday, September 22, 14
  17. 17. Area Formulas Where are some places that you find these formulas? Monday, September 22, 14
  18. 18. Example 1 Make four drawings (using a straight edge) so that two of your drawings are polygons and two are not. Label which is which. Polygons Not Polygons Monday, September 22, 14
  19. 19. Example 1 Make four drawings (using a straight edge) so that two of your drawings are polygons and two are not. Label which is which. Polygons Not Polygons Monday, September 22, 14
  20. 20. Example 1 Make four drawings (using a straight edge) so that two of your drawings are polygons and two are not. Label which is which. Polygons Not Polygons Monday, September 22, 14
  21. 21. Example 1 Make four drawings (using a straight edge) so that two of your drawings are polygons and two are not. Label which is which. Polygons Not Polygons Monday, September 22, 14
  22. 22. Example 1 Make four drawings (using a straight edge) so that two of your drawings are polygons and two are not. Label which is which. Polygons Not Polygons Monday, September 22, 14
  23. 23. Polygon Names 3 sides: 4 sides: 5 sides: 6 sides: 7 sides: 8 sides: Monday, September 22, 14
  24. 24. Polygon Names 3 sides: 4 sides: 5 sides: Triangle 6 sides: 7 sides: 8 sides: Monday, September 22, 14
  25. 25. Polygon Names 3 sides: 4 sides: 5 sides: Triangle 6 sides: 7 sides: 8 sides: Monday, September 22, 14
  26. 26. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral 6 sides: 7 sides: 8 sides: Monday, September 22, 14
  27. 27. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral 6 sides: 7 sides: 8 sides: Monday, September 22, 14
  28. 28. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral Pentagon 6 sides: 7 sides: 8 sides: Monday, September 22, 14
  29. 29. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral Pentagon 6 sides: 7 sides: 8 sides: Monday, September 22, 14
  30. 30. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral Pentagon 6 sides: 7 sides: 8 sides: Hexagon Monday, September 22, 14
  31. 31. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral Pentagon 6 sides: 7 sides: 8 sides: Hexagon Monday, September 22, 14
  32. 32. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral Pentagon 6 sides: 7 sides: 8 sides: Hexagon Heptagon Monday, September 22, 14
  33. 33. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral Pentagon 6 sides: 7 sides: 8 sides: Hexagon Heptagon Monday, September 22, 14
  34. 34. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral Pentagon 6 sides: 7 sides: 8 sides: Hexagon Heptagon Octagon Monday, September 22, 14
  35. 35. Polygon Names 3 sides: 4 sides: 5 sides: Triangle Quadrilateral Pentagon 6 sides: 7 sides: 8 sides: Hexagon Heptagon Octagon Monday, September 22, 14
  36. 36. Polygon Names 9 sides: 10 sides: 12 sides: Monday, September 22, 14
  37. 37. Polygon Names 9 sides: 10 sides: 12 sides: Nonagon Monday, September 22, 14
  38. 38. Polygon Names 9 sides: 10 sides: 12 sides: Nonagon Monday, September 22, 14
  39. 39. Polygon Names 9 sides: 10 sides: 12 sides: Nonagon Decagon Monday, September 22, 14
  40. 40. Polygon Names 9 sides: 10 sides: 12 sides: Nonagon Decagon Monday, September 22, 14
  41. 41. Polygon Names 9 sides: 10 sides: 12 sides: Nonagon Decagon Dodecagon Monday, September 22, 14
  42. 42. Polygon Names 9 sides: 10 sides: 12 sides: Nonagon Decagon Dodecagon Monday, September 22, 14
  43. 43. Example 2 Draw a concave hexagon. Then draw a convex octagon. Monday, September 22, 14
  44. 44. Example 2 Draw a concave hexagon. Then draw a convex octagon. Monday, September 22, 14
  45. 45. Example 2 Draw a concave hexagon. Then draw a convex octagon. Monday, September 22, 14
  46. 46. Example 2 Draw a concave hexagon. Then draw a convex octagon. Monday, September 22, 14
  47. 47. Example 2 Draw a concave hexagon. Then draw a convex octagon. Monday, September 22, 14
  48. 48. Example 3 Draw a regular quadrilateral. Monday, September 22, 14
  49. 49. Example 3 Draw a regular quadrilateral. Monday, September 22, 14
  50. 50. Example 4 Identify the figure based on the number of sides. Is it concave or convex? Is it equilateral, equiangular, or neither? Monday, September 22, 14
  51. 51. Example 4 Identify the figure based on the number of sides. Is it concave or convex? Is it equilateral, equiangular, or neither? Decagon Monday, September 22, 14
  52. 52. Example 4 Identify the figure based on the number of sides. Is it concave or convex? Is it equilateral, equiangular, or neither? Decagon Equilateral, but not equiangular Monday, September 22, 14
  53. 53. Example 4 Identify the figure based on the number of sides. Is it concave or convex? Is it equilateral, equiangular, or neither? Decagon Concave Equilateral, but not equiangular Monday, September 22, 14
  54. 54. Example 5 Find the perimeter of a rectangle whose length is 8.3 cm and width is 3.2 cm. Monday, September 22, 14
  55. 55. Example 5 Find the perimeter of a rectangle whose length is 8.3 cm and width is 3.2 cm. Monday, September 22, 14
  56. 56. Example 5 Find the perimeter of a rectangle whose length is 8.3 cm and width is 3.2 cm. 8.3 cm Monday, September 22, 14
  57. 57. Example 5 Find the perimeter of a rectangle whose length is 8.3 cm and width is 3.2 cm. 8.3 cm 3.2 cm Monday, September 22, 14
  58. 58. Example 5 Find the perimeter of a rectangle whose length is 8.3 cm and width is 3.2 cm. 8.3 cm 3.2 cm P = 2l + 2w Monday, September 22, 14
  59. 59. Example 5 Find the perimeter of a rectangle whose length is 8.3 cm and width is 3.2 cm. 8.3 cm 3.2 cm P = 2l + 2w = 2(8.3) + 2(3.2) Monday, September 22, 14
  60. 60. Example 5 Find the perimeter of a rectangle whose length is 8.3 cm and width is 3.2 cm. 8.3 cm 3.2 cm P = 2l + 2w = 2(8.3) + 2(3.2) = 16.6 + 6.4 Monday, September 22, 14
  61. 61. Example 5 Find the perimeter of a rectangle whose length is 8.3 cm and width is 3.2 cm. 8.3 cm 3.2 cm P = 2l + 2w = 2(8.3) + 2(3.2) = 16.6 + 6.4 = 23 Monday, September 22, 14
  62. 62. Example 5 Find the perimeter of a rectangle whose length is 8.3 cm and width is 3.2 cm. 8.3 cm 3.2 cm P = 2l + 2w = 2(8.3) + 2(3.2) = 16.6 + 6.4 = 23 cm Monday, September 22, 14
  63. 63. Example 6 Find the circumference of a circle with a diameter of 14 in. Monday, September 22, 14
  64. 64. Example 6 Find the circumference of a circle with a diameter of 14 in. Monday, September 22, 14
  65. 65. Example 6 Find the circumference of a circle with a diameter of 14 in. 14 in. Monday, September 22, 14
  66. 66. Example 6 Find the circumference of a circle with a diameter of 14 in. 14 in. C = 2π r = π d Monday, September 22, 14
  67. 67. Example 6 Find the circumference of a circle with a diameter of 14 in. 14 in. C = 2π r = π d C = π d Monday, September 22, 14
  68. 68. Example 6 Find the circumference of a circle with a diameter of 14 in. 14 in. C = 2π r = π d C = π d C = π (14) Monday, September 22, 14
  69. 69. Example 6 Find the circumference of a circle with a diameter of 14 in. 14 in. C = 2π r = π d C = π d C = π (14) C ≈ 43.98 in. Monday, September 22, 14
  70. 70. Problem Set Monday, September 22, 14
  71. 71. Problem Set p. 61 #1-27 odd, 44-47 “Nobody got anywhere in the world by simply being content.” - Louis L’Amour Monday, September 22, 14
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