1 / 59

Math 8 Unit 8

Math 8 Unit 8. Strand 4: Concept 1 Geometric Properties. Polygons and Measurement. PO 2. Draw three-dimensional figures by applying properties of each PO 3. Recognize the three-dimensional figure represented by a net

klarson
Download Presentation

Math 8 Unit 8

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Math 8 Unit 8 Strand 4: Concept 1 Geometric Properties Polygons and Measurement PO 2. Draw three-dimensional figures by applying properties of each PO 3. Recognize the three-dimensional figure represented by a net PO 4. Represent the surface area of rectangular prisms and cylinders as the area of their net. PO 5. Draw regular polygons with appropriate labels Strand 4: Concept 4 Measurement PO 1. Solve problems for the area of a trapezoid. PO 2. Solve problems involving the volume of rectangular prisms and cylinders. PO 3. Calculate the surface area of rectangular prisms or cylinders. PO 4. Identify rectangular prisms and cylinders having the same volume.

  2. Key Terms • Def: Polygon: a closed plane figure formed by 3 or more segments that do not cross each other. Def: Regular Polygon: a polygon with all sides and angles that are equal. Def: Interior angle: an angle inside a polygon Def: Exterior angle: an angle outside a polygon

  3. Triangle • 3 Sides • 3 Angles • Sum of Interior Angles 180 • Each angle measures 60 if regular.

  4. Quadrilateral • 4 Sides • 4 Angles • Sum of Interior Angles 360 • Each angle measures 90 if regular.

  5. Pentagon • 5 Sides • 5 Angles • Sum of Interior Angles 540 • Each angle measures 108 if regular.

  6. Hexagon • 6 Sides • 6 Angles • Sum of Interior Angles 720 • Each angle measures 120 if regular.

  7. Heptagon • 7 Sides • 7 Angles • Sum of Interior Angles 900 • Each angle measures 128.6 if regular.

  8. Octagon • 8 Sides • 8 Angles • Sum of Interior Angles 1080 • Each angle measures 135 if regular.

  9. Nonagon • 9 Sides • 9 Angles • Sum of Interior Angles 1260 • Each angle measures 140 if regular.

  10. Decagon • 10 Sides • 10 Angles • Sum of Interior Angles 1440 • Each angle measures 144 if regular.

  11. Formula: Sum of Interior Angles = 180 (n-2)

  12. Example: Find the sum of the interior angles in the given polygon. • a. 14-gon • b. 20-gon 180(n-2) 180(n-2) 180(20-2) 180(14-2) 180●18 180●12 Total = 3240  Total = 2160 

  13. Example: Find the measure of each angle in the given regular polygon. b. 12-gon • a. 16-gon 180(n-2) 180(n-2) 180(12-2) 180(16-2) 180●10 180●14 Total = 1800  Total = 2520  1800 ÷12 2520 ÷16 150  157.5 

  14. Formula: Sum of Exterior Angles Is always 360

  15. Example: Find the length of each side for the given regular polygon and the perimeter. a.) rectangle, perimeter 24 cm 24 ÷ 4 6 cm b.) pentagon, 55 m 55 ÷ 5 11 m

  16. Example: Find the length of each side for the given regular polygon and the perimeter. c.) nonagon, 8.1 ft 8.1 ÷ 9 0.9 ft d. heptagon, 56 mm 56 ÷ 7 8 mm

  17. Perimeter Evil mathematicians have created formulas to save you time. But, they always change the letters of the formulas to scare you! • Any shape’s “perimeter” is the outside of the shape…like a fence around a yard.

  18. Perimeter • To calculate the perimeter of any shape, just add up “each” line segment of the “fence”. • Triangles have 3 sides…add up each sides length. 8 8 8+8+8=24 The Perimeter is 24 8

  19. Perimeter • A square has 4 sides of a fence 12 12 12 12+12+12+12=48 12

  20. Regular Polygons • Just add up EACH segment 10 8 sides, each side 10 so 10+10+10+10+10+10+10+10=80

  21. Area • Area is the ENTIRE INSIDE of a shape • It is always measured in “squares” (sq. inch, sq ft)

  22. Different Names/Same idea • Length x Width = Area • Side x Side = Area • Base x Height = Area

  23. Notes 3-D Shapes • Base: • Top and/or bottom of a figure. Bases can be parallel. • Edge: • The segments where the faces meet. • Face: • The sides of a three-dimensional shape. • Nets: Are used to show what a 3-D shape would look like if we unfolded it.

  24. Prisms • Have Rectangles for faces • Named after the shape of their Bases

  25. More Nets

  26. Fun with Prisms by D. Fisher

  27. Triangular Prism Vertices (points) 6 Edges (lines) 9 Faces (planes) 5 The base has3sides.

  28. Rectangular Prism 4 The base has sides. Vertices (points) 8 Edges (lines) 12 Faces (planes) 6

  29. Pentagonal Prism The base has sides. 5 Vertices (points) 10 Edges (lines) 15 Faces (planes) 7

  30. Hexagonal Prism 6 The base has sides. Vertices (points) 12 Edges (lines) 18 Faces (planes) 8

  31. Octagonal Prism The base has sides. 8 Vertices (points) 16 Edges (lines) 24 Faces (planes) 10

  32. Pyramids • Have Triangles for faces • Named after the shape of their bases.

  33. Fun with Pyramids By D. Fisher

  34. Triangular Pyramid Vertices (points) 4 Edges (lines) 6 Faces (planes) 4 The base has 3 sides.

  35. Square Pyramid Vertices (points) The base has sides. 4 5 Edges (lines) 8 Faces (planes) 5

  36. Pentagonal Pyramid Vertices (points) The base has sides. 5 6 Edges (lines) 10 Faces (planes) 6

  37. Hexagonal Pyramid Vertices (points) The base has sides. 6 7 Edges (lines) 12 Faces (planes) 7

  38. Octagonal Pyramid Vertices (points) The base has sides. 8 9 Edges (lines) 16 Faces (planes) 9

  39. Name Picture Base Vertices Edges Faces Triangular Pyramid Square Pyramid Pentagonal Pyramid Hexagonal Pyramid Heptagonal Pyramid Octagonal Pyramid 3 4 6 4 4 5 8 5 5 6 10 6 6 7 12 7 7 8 14 8 Draw it 8 9 16 9 No picture n n + 1 2n n + 1 Any Pyramid

  40. Name Picture Base Vertices Edges Faces Triangular Prism Rectangular Prism Pentagonal Prism Hexagonal Prism Heptagonal Prism Octagonal Prism 3 6 9 5 4 8 12 6 5 10 15 7 6 12 18 8 7 14 21 9 Draw it 8 16 24 10 No picture n 2n 3n n + 2 Any Prism

  41. Cylinder • Circles for bases • Rectangle for side

  42. Points of View View point is looking down on the top of the object. View point is looking from the right (or left) of the object. View point is looking up on the bottom of the object.

  43. Top Top View Front Side Front View Side View Side Front Bottom View Bottom Example 1 :

  44. D q H Front View Example 2 : Top Left View

  45. Example 3 : Top view Front View Left View

  46. Front View Example 4 Top View Left View Bottom View

  47. Surface Area • Surface Area: the total area of a three-dimensional figures outer surfaces. • Surface Area is measured in square units (ex: cm2)

  48. h h w l l l w w h w h RectangularPrism SA=2lw +2lh + 2wh

  49. 1. Find the surface area. H SA=2lw +2lh + 2wh L W SA=248 + 242+ 282 SA= 64 + 16+ 32 SA= 112 cm2

  50. 2. Find the surface area of a box with a length of 6 in, a width of 6 inches and a height of 10 inches. SA=2lw +2lh + 2wh SA=266 + 2610+ 2610 SA= 72 + 120+ 120 SA= 312 cm2

More Related