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12.1– Explore Solids

12.1– Explore Solids. Polyhedron:. A solid that is bounded by polygons. Faces:. Polygon on the side of the shape. Ex:. Hex ABCDFE. Quad EFKL. Edges:. Where two polygons meet to form a line. Ex:. Vertex:. Where 3 polygons meet to form a point. Ex:. Non-Polyhedron:.

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12.1– Explore Solids

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  1. 12.1– Explore Solids

  2. Polyhedron: A solid that is bounded by polygons

  3. Faces: Polygon on the side of the shape Ex: Hex ABCDFE Quad EFKL

  4. Edges: Where two polygons meet to form a line Ex:

  5. Vertex: Where 3 polygons meet to form a point Ex:

  6. Non-Polyhedron: An edge that isn’t a polygon

  7. Base: Polygon the solid is named after.

  8. Lateral Faces: Parallelograms or triangles on the sides of the solid

  9. Prism: Polyhedron with two parallel, congruent bases Named after its base

  10. Pyramid: Polyhedron with one base and lateral faces Named after its base.

  11. Regular: All of the faces are congruent regular polygons

  12. Convex: Any two points on its surface can be connected by a segment that lies entirely inside or on the solid (rubberband)

  13. A side of the solid goes inward Concave:

  14. Cross Section: Intersection of a plane and a solid

  15. Euler’s Theorem: Faces + Vertices = Edges + 2 F + V = E + 2

  16. Platonic Solids: Regular Polyhedra, only 5. Named after how many faces they have

  17. 4 faces Regular Tetrahedron:

  18. 6 faces Cube:

  19. 8 faces Regular Octahedron:

  20. 12 faces Regular Dodecahedron:

  21. 20 faces Regular Icosahedron:

  22. Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning. curved sides No,

  23. Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning. Yes, Rectangular prism

  24. Determine whether the solid is a polyhedron. If it is, name the polyhedron. Explain your reasoning. curved sides No,

  25. Use Euler’s Theorem to find the value of n. F + V = E + 2 n + 8 = 12 + 2 n + 8 = 14 n = 6

  26. Use Euler’s Theorem to find the value of n. F + V = E + 2 5 + 6 = n + 2 11 = n + 2 9 = n

  27. Use Euler’s Theorem to find the value of n. F + V = E + 2 8 + n = 18 + 2 8 + n = 20 n = 12

  28. Find the number of faces, vertices, and edges of the polyhedron. Check your answer using Euler’s Theorem. F + V = E + 2 5 + 6 = 9 + 2 11 = 11 F = 5 V = 6 E = 9

  29. Find the number of faces, vertices, and edges of the polyhedron. Check your answer using Euler’s Theorem. F + V = E + 2 6 + 8 = 12 + 2 14 = 14 F = 6 V = 8 E = 12

  30. Find the number of faces, vertices, and edges of the polyhedron. Check your answer using Euler’s Theorem. F + V = E + 2 6 + 6 = 10 + 2 12 = 12 F = 6 V = 6 E = 10

  31. Sketch the polyhedron. Cube

  32. Sketch the polyhedron. Rectangular prism

  33. Sketch the polyhedron. Pentagonal pyramid

  34. Determine if the solid is convex or concave. convex

  35. Determine if the solid is convex or concave. concave

  36. Determine if the solid is convex or concave. convex

  37. Describe the cross section formed by the intersection of the plane and the solid. pentagon

  38. Describe the cross section formed by the intersection of the plane and the solid. circle

  39. Describe the cross section formed by the intersection of the plane and the solid. triangle

  40. HW Problems #31 Ans: D

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