1. GEOMETRY LESSON 10-1
Space Figures and Nets
Is the pattern a net for a cube? If so, name two letters that will be on opposite faces.
The pattern is a net because you can fold it to form a cube. Fold squares A and C up to form the back and front of the cube. Fold D up to form a side. Fold E over to form the top. Fold F down to form another side.
After the net is folded to form a cube, the following pairs of letters are on opposite faces:
A and C are the back and front faces.
B and E are the bottom and top faces.
D and F are the right and left side faces.

2. GEOMETRY LESSON 10-1
Space Figures and Nets
Draw a net for the figure with a square base and four isosceles triangle faces. Label the net with its dimensions.
Think of the sides of the square base as hinges, and “unfold” the figure at these edges to form a net.
The base of each of the four isosceles triangle faces is a side of the square.

3. GEOMETRY LESSON 10-1
Space Figures and Nets
Use Euler’s Formula to find the number of edges on a solid with 6 faces and 8 vertices.
F + V = E + 2 Euler’s Formula
6 + 8 = E + 2 Substitute the number of faces and vertices.
12 = E Simplify.
A solid with 6 faces and 8 vertices has 12 edges.

4. GEOMETRY LESSON 10-1
Space Figures and Nets
Is the pattern a net for a cube? If so, name two letters that will be on
opposite faces.
1. 2.
3. Draw a net for the figure. no
yes; A and C, B and D, E and F
Use Euler’s Formula to solve.
4. A polyhedron with 12 vertices and 30 edges has how many faces? 20
5. A polyhedron with 2 octagonal faces and 8 rectangular faces has how many vertices? 16