1 / 22

Homework, red pen, pencil, gradesheet

Learn about calculating surface area of 3D figures using formulas, and classify polyhedra based on their faces. Practice problems included.

rrandolph
Download Presentation

Homework, red pen, pencil, gradesheet

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. Have Out: Homework, red pen, pencil, gradesheet 7/11/12 Bellwork: Find the Area 2 h2 = 122 + 92 (Pythagorean. Thm.) 15 ft h2 = 144+ 81 h 10 ft h = 15 ft P = 2 + 15 + 10 + 24 + 15 24 ft = 66 ft.

  2. 2 15 ft 1 Picture Equation Formulas 2 10 ft 3 Simplify Solve 4 24 ft A = + 10 12 15 9 1 = (10  15) + ( 12  9) 2 = 150 + 54 = 204 ft2

  3. Surface Area: Add the area of every side

  4. ) ( SA = + 2 + 10 8 8 12 18 9 Net: 3-D figure unfolded (Helps you see all the sides) = (½• 10 • 12)+ 2(½ • 18 • 8) + (½ • 9 • 8) = (60) + 2(72) + (36) = 60 + 144 + 36 = 240 u2

  5. Add to your notes... Total Surface Area: The sum of the areas of EACH of the faces of a polyhedron. We can set up TSA problems just like we did the area subproblems! One equation…four steps: 1. Picture Equation 2. Formulas 3. Simplify 4. Solve & Answer with correct units. What type of units would be correct for Total Surface Area? units2

  6. How many faces does the Rectangular Pyramid on the resource page have? ) ( 20 TSA = + 4 15 15 15 SV-101 5 1. Picture Equation = (15 • 15) + 4(½ • 20 • 15) 2. Formulas = (225) + 4(150) 3. Simplify = 225 + 600 4. Solve & Answer with correct units. = 825 u2

  7. Add to your notes: Rectangular Pyramid PYRAMID Base: Polygon on the bottom base The shape of the base gives the figure it’s name lateral faces Lateral faces: Triangles that connect the base to one point at the top. (vertex) The lateral faces are not always the same size base Hexagonal Pyramid

  8. 12’ 10’ 10’

  9. Add to your notes: A PRISM is: base 2 congruent (same size and shape) parallelbases that are polygons height 3) lateral faces (faces on the sides) that are parallelograms formed by connecting the corresponding vertices of the 2 bases. base lateral faces Lateral faces may also be rectangles, rhombi, or squares.

  10. On your paper, shade the figure that is the base for each of the following solids. Then name the solid using the name of its polygonal base and either prism or pyramid. triangular prism rectangular, square, or parallelogram prism pentagonal prism hexagonal prism triangular pyramid octagonal prism pentagonal pyramid rectangular, square, or trapezoidal pyramid Rectangular or parallelogram prism triangular prism hexagonal pyramid pentagonal prism

  11. 8 4 ( ) ) ( ) ( TSA = 2 + 2 + 2 8 4 4 8 20 20 V= • 20 = (84)(20) = (32)(20) = 640 u3 10 = 2(4 • 8)+ 2(4 • 20) + 2(20 • 8) = 2(32) + 2(80) + 2(160) = 64 + 160 + 320 = 544 u2

  12. 1. 2. 12 in 5 in 15 in 12 cm 13 in Area of Octagon =52 cm2 12 V= • 12 V= • 15 5 = (52)(12) = (½ 12 • 5)(15) = 624 cm3 = (30)(15) = 450 in3

  13. SV-83 Polyhedra Add to your notes... Polyhedron: A 3-dimensional object, formed by polygonal regions, that has no holes in it. Plural: polyhedra face: A polygonal region of the polyhedron. edge: A line segment where two faces meet. vertex: A point where 3 or more sides of faces meet. Plural: vertices faces vertices edges

  14. SV-83 These are polyhedra: These are NOT polyhedra:

  15. SV-84 Classify the following as a polyhedron or not a polyhedron. Write YESor NO. If no, explain why not. YES YES NO The face has a curve, which is not a polygon. NO It is only 2-dimensional. YES It is only 2-dimensional. NO The face has a curve, which is not a polygon. It is only 2-dimensional. NO NO YES

  16. SV-84 Polyhedra are classified by the number of faces they have. Here are some of their names: 9 faces 4 faces tetrahedron nonahedron 10 faces 5 faces pentahedron decahedron 11 faces 6 faces hexahedron undecahedron 12 faces 7 faces heptahedron dodecahedron 20 faces 8 faces octahedron icosahedron Be familiar with these names.

  17. SV-79 Complete your resource page by counting the total number of vertices, edges, and faces for each polyhedron. Then, use the information you found to answer SV-80

  18. 4 6 4 8 8 12 6 14 6 12 8 14 12 18 8 20 10 15 7 17 20 30 12 32

  19. SV-80 Let VR = number of vertices, E = number of edges, and F = number of faces. In 1736, the great Swiss mathematician Ledonhard Euler found a relationship among VR, E, and F. A) For each row, calculate VR + F. See resource page. • Write an equation relating VR, F, and E. VR + F = E + 2 Ledonhard Euler 1707-1783

  20. SV-81 Is it possible to make a tetrahedron with non-equilateral faces? If not, explain why not. If so, draw a sketch. Yes it is possible. Shorten the length of any one edge. Possible examples:

  21. SV-82 How many edges does the solid have? (Don’t forget the ones you can’t see.) There are 9 edges. How many vertices does it have? There are 6 vertices.

More Related