Look at page 193 in your Look at page 193 in your explorations book.explorations book.

Ignore the letters--they are not used for this.Ignore the letters--they are not used for this.

Each figure is made up of 5 squares that may or Each figure is made up of 5 squares that may or may not be able to form 5 sides of a cube.may not be able to form 5 sides of a cube.

We call this a net. We call this a net.

Which of the 12 nets will form a cube?Which of the 12 nets will form a cube?

Polyhedra• On your tables, you will find sets of

polyhedra. Examine them.• Compare and contrast polyhedra and

polygons.• What is true about all prisms?• What is true about all pyramids?• What is true about prisms and pyramids, but

not about other polyhedra?

Attributes• In a polygon, we call it a side. In a

polyhedron, we call it a(n) __________.• In a polygon, we call it a vertex. In a

polyhedron, we call it a(n) __________.• In a polygon, there is one plane interior, and

so we do not name it. In a polyhedron, there are many plane interiors, and we call them __________.

Exploration 8.15• Do Part 1 #1 and 2 for figures a - d and g. • Create the 5 regular polyhedra--cut out the

nets and tape the sides together. Then, mark or color the vertices, edges, and faces. Record their numbers as well.

• Can you identify a relationship between the faces, edges, and vertices of all these polyhedra?

Constructing and Deconstructing Solids

• A solid is formed by a 3-dimensional figure and its interior.

• Because a solid has 3 dimensions, it is easy to miss hidden aspects when viewed from only one perspective. Hence, we typically draw using 3 views: front, side, and top.

Let’s do one together.• Front Side Top

Try these other two• Front Right Side Top

Draw the views• Front

• Right Side

• Top

Nets• When we think of polyhedra, we think

of the 3-dimensional figure. • If we wanted to find the surface area, it

would help if we could spread it out and look at it in 2-dimensions.

• To do this, we find the net of the polyhedron.

Nets• Exploration 8.19 Part 3• Examine each of the nets. • Without cutting or folding, determine the type

of 3-dimensional figure it will create.• Last, draw another net that will create the

same 3-dimensional figure. If it is not possible, explain why not.

Solids• Prisms: cubes, rectangular, triangular,

etc… A polyhedron and its interior.– Named for their bases. A triangular prism

has 2 bases that are triangles.– Top and bottom bases are parallel and

congruent.– Faces are all rectangles with the same

height.

Solids• Cylinders:

– Like prisms, but with 2 bases that are circles.

– One other face in the shape of a rectangle.

Solids• Pyramids: square, triangular,

hexagonal, etc.– Named for the base.– Has just one base, and the other faces are

triangles.– The height of the triangle faces is called

the slant height.

Solids• Cones:

– Like pyramids, but with a circular base.– Face is a sector of a circle.– Top point is called an apex.

• Spheres: No faces or bases. “Equator” is known as a great circle.