1. Surface Area and Volume
Chapter 12

2. Exploring Solids 12.1 California State Standards Lesson goals
8, 9: Solve problems involving the surface area and lateral area of geometric solids and COMMIT TO MEMORY THE NECESSARY FORMULAS.
Identify Polyhedrons
Apply Euler’s Theorem

3. definition Polyhedron edge face face vertex
Plural: polyhedra
Polyhedron
A 3-dimensional solid figure formed by polygons.
Faces: the polygons that form the polyhedron
Edges: a line segment formed by the
intersection of two faces.
Vertex: the point where 3 or more edges meet.
face
edge
face
vertex

4. examples
Polyhedra
Prism
Pyramid
Non-Polyhedra
Cylinder
Cone
Sphere

5. definition
Regular Polyhedron
All faces are congruent regular polygons

6. definition Platonic Solids 5 regular, convex polyhedra
Tetrahedron 4 equilateral triangles
Hexahedron 6 squares
Octahedron 8 equilateral triangles
Dodecahedron 12 regular pentagons
Icosahedron 20 equilateral triangles

7. tetrahedron 4 faces hexahedron 6 faces octahedron 8 faces icosahedron
(cube)
octahedron
8 faces
icosahedron
20 faces
dodecahedron
12 faces

8. definition Cross-section The intersection of a plane and a solid.
Describe the cross section.
The cross section is a square.

9. definition Cross-section The intersection of a plane and a solid.
Describe the cross section.
The cross section is a circle.

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

11. example
A polyhedron has 18 edges and 12 vertices. How many faces does it have?

12. Each side is shared by two polygons
example
Find the number of vertices for a polyhedron with 10 faces made from 4 triangles, 1 square, 4 hexagons, and 1 octagon.
Each side is shared by two polygons

13. Each side is shared by two polygons
example
A soccer ball is made of 12 pentagons and 20 hexagons. How many vertices does the soccer ball have?
Each side is shared by two polygons

14. Definition
Net
the two-dimensional representation of a three-dimensional figure.
back
left
roof
right
left
side
right
bottom
front
What would the polyhedron look like if laid flat?

15. Remember: this is called a NET.
example
What would the cylinder look like laid flat?
top
“label”
bottom
Remember: this is called a NET.

16. Today’s Assignment
p. 723: 6 – 15, 25 – 31, 47 – 49