1. 2 D or 3 D Learning Objective: Determine the perimeter and area of basic 2 dimensional figuresDetermine the perimeter and area of basic 2 dimensional figures Determine the volume of basic 3 dimensional figuresDetermine the volume of basic 3 dimensional figures Contrast the difference between surface area and volumeContrast the difference between surface area and volume CA Standard: MG: 2.1 Use formulas to find area of basic plane figures MG: 2.3 Students compute the perimeter, area, & volume of common geometric objects & use them to find measures of less common objects.

2. Where are the rectangles?

7. Where are the triangles?

11. Learning Objectives To find the area and perimeter of basic plane figures (squares, rectangles, parallelograms, trapezoids, triangles)To find the area and perimeter of basic plane figures (squares, rectangles, parallelograms, trapezoids, triangles) To find the volume of basic 3 dimensional objects (cube, rectangular prism)To find the volume of basic 3 dimensional objects (cube, rectangular prism) To explain the difference between surface area and volumeTo explain the difference between surface area and volume

12. Quadrilaterals Part One: Rectangles, Squares

13. Quadrilaterals Rectangles Squares 1. Draw It 2. Tell me about the sides (parallel, perpendicular, congruent) 3. Tell me about the angles (acute, obtuse, right)

14. Perimeter and area Perimeter: –Distance around a shape –Units are linear, such as inches or centimeters. Area: –Space in a shape –Units are square units, such as square inches or square centimeters.

18. Formulas for squares, rectangles, and parallelograms Formula for finding perimeter P = 2(base + height) Formula for finding area A = (b)(h)

19. Which are 4-sided polygons? Quadrilaterals Triangles Rectangles Pentagons Squares Rhombus Pyramid Hexagons Prism Kite Circles Trapezoid Cubes Octagon Parallelogram Cylinder

20. Triangles How are they related to parallelograms?

21. Can you split these shapes in half by drawing a diagonal line?

22. How is a triangle different?

23. How do we find perimeter and area?

24. Formula Area of parallelograms, rhombus, rectangle, square = (base)(height) Area of triangles = (base)(height)

25. What if it is not a right triangle? Find the right ( ) Altitude.

26. Quadrilaterals Part Two: Parallelograms, Rhombus

27. Formulas for squares, rectangles, and parallelograms Formula for finding perimeter P = 2(base + height) Formula for finding area A = (b)(h)

29. 2 cm 4 cm 1.5 cm 2 cm 5 cm 4 cm

30. 1.5 cm 2 cm 3 cm 4 cm rotate

31. Quadrilaterals Trapezoids

32. What are Trapezoids? –Quadrilateral with one pair of parallel lines Any special Trapezoids? –An isosceles Trapezoid has one pair of congruent sides.

33. Formula for Area of Trapezoid Formula for finding area A = (h)(b 1 + b 2 )

34. Formula for Area of Trapezoid 14 in 11 in 10 in 11 in

35. Formula for Area of Trapezoid 12 in 10 in 9 in 8 in

36. Formula for Area of Trapezoid 14 in 10 in 9.5 in 8 in 8.5 in

37. Circles In math, art, and all around us

39. http://home.comcast.net/~eschermc/Circle_Limit_III.jpg

40. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html ”Flemming’s rules" Something appears to run in the circular clouds (visual phantoms).

41. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html ”Falling snow" The figure appears to scintillate

42. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html ”Rokuyo stars*” *Ryokuyo is a kind of week made up of 6 days. Six white circles appear to scintillate. Moreover, red circles appear to rotate clockwise while blue ones rotate counterclockwise.

43. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html ”A time tunnel" Color blobs appear to scintillate

44. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html ”Jiggle" The surround appears to jiggle and scintillate

45. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html ”Blue Sun" Circular scintillation appears

46. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html ”Statis gingin shippo" “Gingin” means scintillating and “shippo” means a Japanese traditional pattern

47. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html ”Warp" Stars appear to twinkle when we fixate on the center.

48. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html ”Glare" The rings appear to glare

49. http://www.ritsumei.ac.jp/~akitaoka/opart-e.html "Earthquake" The surround appears to fluctuate.

52. Circles Does a circle have perimeter?  Yes, but we call it circumference Does a circle have area?  Yes

53. Vocabulary Circumference – distance around a circle  C = (pi)(diameter) = π d Area – space inside a circle  A = (pi)(radius 2 ) = πr 2 Arc –part of the curve of a circle Diameter – distance from one side of a circle to another across the center Radius – half of a diameter Center – the middle of a circle Chord – a segment from any point on a circle to another point on the same circle.

54. 20 in 2 cm 1.5 cm

55. What am I? I have four sides with right angles.I have four sides with right angles. I have three congruent sides.I have three congruent sides. I have four congruent sides, two acute angles, two obtuse angles.I have four congruent sides, two acute angles, two obtuse angles. I have four congruent sides.I have four congruent sides. I am closed figure without sides.I am closed figure without sides. I have six congruent faces.I have six congruent faces.

56. 2 D or 3 D 2 D – plane (flat) Vertex Sides Perimeter Area 3 D – solid (depth) Edges Vertices Faces Volume Surface area

57. Plane Vs. Solids

60. 3 Dimensional Objects Surface AreaSurface Area The sum of the areas of the plane faces of a 3 dimensional object measured in square units.The sum of the areas of the plane faces of a 3 dimensional object measured in square units. VolumeVolume The space inside a 3 dimensional object measured in cubic units.The space inside a 3 dimensional object measured in cubic units.

61. Prisms Surface area is measured by finding the sum of the areas of each face.Surface area is measured by finding the sum of the areas of each face. Volume is calculated by multiplying the area of the base times the height.Volume is calculated by multiplying the area of the base times the height.

62. Prisms 20 ft 5 ft 8 ft 3 in

63. Cylinder Surface area is measured by finding the area of each face and adding them up.Surface area is measured by finding the area of each face and adding them up. A = 2(π r 2 ) + (π)(d)(h) unwrapped

64. Cylinder Volume is calculated by multiplying the area of the base times the height.Volume is calculated by multiplying the area of the base times the height. V = (π r 2 )(h)

65. Cylinders 15 in 6 in

66. Cylinders 6 in. 2 in.