1. 12.1– Explore Solids

2. Polyhedron:
A solid that is bounded by polygons

3. Non-Polyhedron:
An edge that isn’t a polygon
No Curves!

4. Prism:
Polyhedron with two parallel, congruent bases
Named after its base.
Triangular Prism
Hexagonal Prism

5. Pyramid:
Polyhedron with one base.
Named after its base.
Rectangular Pyramid
Pentagonal Pyramid

6. Base:
Polygon the solid is named after.
Hexagon
Rectangle

7. Lateral Face:
Parallelograms or triangles on the sides of the solid

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

9. Concave:
A side of the solid goes inward

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

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

12. Platonic Solids:
Regular Polyhedra, only 5. Named after how many polygons they have containing the shape

13. Regular Tetrahedron:
4 polygons

14. Cube:
6 polygons

15. Regular Octahedron:
8 polygons

16. Regular Dodecahedron:
12 polygons

17. Regular Icosahedron:
20 polygons

18. Faces:
Polygons containing the solid
Ex:
Hex ABCDFE

19. Faces:
Polygons containing the solid
Ex:
Hex ABCDFE
Quad EFKL

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

21. Vertex:
Where 3 polygons meet to form a point
(the corners)
Ex:

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

23. 1. Tell whether the solid is a polyhedron
1. Tell whether the solid is a polyhedron. If it is, find the number of faces, vertices, and edges.
Polyhedron: YES or NO
Faces: ___________
Vertices: _________
Edges: ___________ 6 6 10
F + V = E + 2
6 + 6 =
12 = 12

24. 1. Tell whether the solid is a polyhedron
1. Tell whether the solid is a polyhedron. If it is, find the number of faces, vertices, and edges.
Polyhedron: YES or NO
Faces: ___________
Vertices: _________
Edges: ___________ 6 8 12
F + V = E + 2
6 + 8 =
14 = 14

25. 1. Tell whether the solid is a polyhedron
1. Tell whether the solid is a polyhedron. If it is, find the number of faces, vertices, and edges.
Polyhedron: YES or NO
Faces: ___________
Vertices: _________
Edges: ___________

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

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

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

29. Shape: __________________ Hexagonal Pyramid
3. Identify the base of the polyhedron, then name the given shape.
Hexagon
Base: ____________
Shape: __________________
Hexagonal Pyramid

30. Shape: __________________ Rectangular Prism
3. Identify the base of the polyhedron, then name the given shape.
Rectangle
Base: ____________
Shape: __________________
Rectangular Prism

31. Shape: __________________ Triangular Prism
3. Identify the base of the polyhedron, then name the given shape.
Triangle
Base: ____________
Shape: __________________
Triangular Prism

32. Shape: __________________
3. Identify the base of the polyhedron, then name the given shape.
Rectangle
Base: ____________
Shape: __________________
Rectangular Pyramid

33. Shape: __________________ Hexagonal Prism
3. Identify the base of the polyhedron, then name the given shape.
Hexagon
Base: ____________
Shape: __________________
Hexagonal Prism

34. Shape: __________________
3. Identify the base of the polyhedron, then name the given shape.
Heptagon
Base: ____________
Shape: __________________
Heptagonal Pyramid

35. Determine if the solid is convex or concave.

36. Determine if the solid is convex or concave.

37. Determine if the solid is convex or concave.

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

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

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

41. HW Problems
12.1
3-6, odd, 22-24, 31, 32
#31
Ans: D