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Chapter 9 and 10 Journal

Chapter 9 and 10 Journal. Marcela Janssen. areas. Areas. Trapezoid (base1 x base2)h 2 Kite (½ diagonal2) diagonal 1 Rhombus (½ diagonal2) diagonal 1 Any polygon with any # of sides Area = (½ sa ) n. Square base x height Rectangle base x height

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Chapter 9 and 10 Journal

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  1. Chapter 9 and 10Journal Marcela Janssen

  2. areas

  3. Areas • Trapezoid(base1 x base2)h 2 • Kite(½ diagonal2) diagonal 1 • Rhombus (½ diagonal2) diagonal 1 • Anypolygonwithany # of sidesArea = (½ sa) n • Squarebase x height • Rectanglebase x height • Trianglebase x height 2 • Parallelogrambase x height

  4. Examples Area 9m 9m x 3m 27m2 3m 6mm 6mm x 4mm 4mm 2 24/2 = 12mm2

  5. Composite figures

  6. Composite figures Composite Figure: A plane figure made up of triangles, rectangles, trapezoids, circles, orother simple shapesor a three dimensional-figure made up of prisms, cones, pyramids, cylinders and other simple three-dimensional figures. Plane figure Tridimensional composite figure

  7. Tofindthearea of a composite figure: • Divide tha figure into simple shapes • Findtheareas of the simple shapes • Addall of theareas of the simple shapestogetthearea of thewholecomposite figure

  8. Example 6cm Ill 7 cm 1 cm 2 cm 12 cm (10 x 6)2 2 120 2 60 cm 12x 2 24 60 + 24 84 cm 2

  9. Areas of circles

  10. Areas of Circles • Tofindthearea of a circlejust use theequation: Area = π r 2

  11. SOLIDS

  12. Solids A solidis a three-dimensional figure. Sphere Triangular prism Rectangular ppyramid

  13. PRISM

  14. Prisms Prism: isformedby 2 ll congruentpolygonal faces called bases by faces that are parallelogram. Differencebewteen a prism and a pyramid:

  15. Whatdoesit look like?

  16. Tofindthesurfacearea of a prism: Surface Area = (perimeter of base) L + 2(Area of base) Example: Surface A. = (16m) 7 + 2(24m2) 112 + 48 160 m2

  17. A net is a diagram of thesurfaces of a tridimensiitionalobject,

  18. AREA OF CYLINDER

  19. Cylinders Isformedbytwoparallelcongruent circular bases and a curvedsurfacethatconnectsthe bases. Tofindthesurfacearea: SurfaceArea = 2(π r 2) + (2π r)h

  20. Examples

  21. AREA OF PYRAMID NOT EXAMPLES

  22. Pyramid Tofindthe total surfacearea: ½ pl + b L= lenght of the lateral face A= area of the base P= perimeteropfthe base

  23. AREA OF CONE NOT EXAMPLES

  24. Cone Tofindthesurfacearea of a cone: π r√r2 +h2 R= radius H = height

  25. AREA OF CUBE

  26. Cube A cube is a squareprismwith 6 congruent faces. Tofindthesurfacearea: 6 a 2 A = lenght of edges

  27. Example 1 Surface Area = 6(5 in)2 = 6(25) = 150 in2

  28. Example 2 Given that the height of a cube is 5 ft 3 in what is the surface area that it has? Surface Area = 6(5 ft 3 in)2 = 6(63 in) = 6(63) = 378 in2 = 31.5 ft2

  29. Example 3 Howmuchisthesurfacearea of thisrubiks cube? Surface Area = 6(8 in)2 = 6(64) = 384 in2

  30. CAVALIERI’S PRINCIPLE

  31. Cavalieri’sPrinciple • Iftwothree-dimensional figures havethesame base area, and sameheight, theywillhavethesamevolume.

  32. VOLUMES

  33. Volume • Prism • Cylinder πr2 • Pyramid 1/3 bh Cone 1/3 π r2 h

  34. SPHERES

  35. Spheres Sphere: A tridimensional solidcreatedbyallpointsequidistant (radius) fromthe center point. Hemisphere: Half of a sphere Great Circle: Any line drawnaroudthespherethatcutsitintotwohemisphere (equator)

  36. Surfacearea of a sphere: 4 π r2 Example: r= 8.5 4π 8.52 4π 17 Volume of a sphere: 4/3 πr3 How many water is needed to fill this sphere with water with a radius of 8.5? 4/3 πr3 4/3 π 8.53 86 mm

  37. TO BE GRADED: • SPHERES • PRISMS • AREA OF A CUBE

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