1. Warm-up
Assemble Platonic Solids

2. Unit XI: Exploring Surface Area and Volume
Students will explore nets of three dimensional figures.
Students will calculate surface area and volume of solid figures, including composite figures.

3. POLYHEDRA (plural for polyhedron)
A polyhedron is a solid bounded by polygons, called faces, that enclose a single region of space.
An edge is a line segment formed by the intersection of two faces.
A vertex is a point where three or more edges meet.

4. Am I a Polyhedron?
rectangles
Faces:
Edges:
Vertices: 6 12 8

5. rectangles and hexagons
Am I a Polyhedron?
rectangles and hexagons
Faces:
Edges:
Vertices: 8 18 12

6. Am I a Polyhedron? hexagon and triangles Faces: 7 Edges: 12 Vertices:

7. Am I a Polyhedron?
No, it does not have faces that are polygons

8. Am I a Polyhedron?
No, it does not have faces that are polygons

9. Am I a Polyhedron?
No, it does not have faces that are polygons

10. Am I a Polyhedron?
No, it does not have faces that are polygons

12. Euler’s Theorem
The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F + V = E + 2.

13. Use the Euler’s Theorem to find the unknown number.
Faces: ____ Vertices: 6 Edges: 12
Faces: 5 Vertices: ___ Edges: 9
Faces: 20 Vertices: 12 Edges: ___ 8 6 30

14. Am I a Polyhedron?
pentagons
Faces:
Edges:
Vertices: 12 30

15. 8 triangles
18 squares
Faces:
Edges:
Vertices: 48

16. Name the number of faces, edges, and vertices of the polyhedron.
Note: This soccer ball has 32 faces, 20 regular hexagons, and 12 pentagons.
Faces: 5
Faces: 32

17. The Five Platonic Solids - Named after the Greek mathematician and philosopher Plato
Regular, convex polyhedron with congruent faces of regular polygons and the same number of faces meeting at each vertex.

18. concave regular irregular convex convex
Regular (if all of its faces are congruent) Concave and Convex Polyhedra
regular
convex
irregular
convex
concave

19. Top View
convex
concave

20. concave
concave

21. Your Turn!!!
A solid has 14 faces; 6 octagons and 8 triangles. How many vertices does it have?