1. 12.1 & 12.2 – Explore Solids & Surface Area of Prisms and Cones

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

13. Concave: A side of the solid goes inward

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. Regular Tetrahedron: 4 faces

18. Cube: 6 faces

19. Regular Octahedron: 8 faces

20. Regular Dodecahedron: 12 faces

21. Regular Icosahedron: 20 faces

22. Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. Rectangular prism Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________ 6 8 12 F + V = E + 2 6 + 8 = 12 + 2 14 = 14

23. Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. curved sides Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________

24. Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. Pentagonal Pyramid Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________ 6 6 10 F + V = E + 2 6 + 6 = 10 + 2 12 = 12

25. Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. Triangular prism Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________ 5 6 9 F + V = E + 2 5 + 6 = 9 + 2 11 = 11

26. Determine whether the solid is a polyhedron. If it is, name the polyhedron and state the number of faces, vertices, and edges. curved side Polyhedron: YES or NO Faces: ___________ Vertices: _________ Edges: ___________

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

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

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

30. Sketch the polyhedron. Cube

31. Sketch the polyhedron. Rectangular prism

32. Sketch the polyhedron. Pentagonal pyramid

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

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

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

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

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

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

39. Cylinder: Prism with circular bases

40. Surface area: Area of each face of solid

41. Lateral area: Area of each lateral face

42. Right Prism: Each lateral edge is perpendicular to both bases

43. Oblique Prism: Each lateral edge is NOT perpendicular to both bases

44. Net: Two-dimensional representation of a solid

45. Surface Area of a Right Prism: SA = 2B + PH B = area of one base P = Perimeter of one base H = Height of the prism H

46. Surface Area of a Right Cylinder: H SA = 2B + PH

47. 1. Name the solid that can be formed by the net. Cylinder

48. 1. Name the solid that can be formed by the net. Triangular prism

49. 1. Name the solid that can be formed by the net. rectangular prism Cube?

50. 2. Find the surface area of the right solid. SA = 2B + PH SA = 2(30) + (22)(7) B = bh B = (5)(6) B = 30 P = 5 + 6 + 5 + 6 P = 22 SA = 60 + 154 SA = 214m2m2

51. 2. Find the surface area of the right solid. SA = 2B + PH SA = 2(30) + (30)(10) P = 5 + 12 + 13 P = 30 SA = 60 + 300 SA = 360cm 2 c 2 = a 2 + b 2 c 2 = (5) 2 + (12) 2 c 2 = 25 + 144 c 2 = 169 c = 13

52. 2. Find the surface area of the right solid. cm 2

53. 2. Find the surface area of the right solid. in 2 144in

54. 3. Solve for x, given the surface area. SA = 2B + PH 142 = 2(5x) + (2x + 10)(7) B = bh B = 5x P = 5 + x + 5 + x P = 2x + 10 142 = 10x + 14x + 70 142 = 24x + 70 72 = 24x 3ft = x

55. 3. Solve for x, given the surface area.