E–3
Name
Date
Pyramid and Prism Patterns
The tables show the number of faces, edges, and vertices of three different types of
prisms and pyramids. Use the tables to answer each question.
Prisms
Pyramids
Triangular
Rectangular
Pentagonal
Triangular
Rectangular
Pentagonal
Faces
5
6
7
Faces
4
5
6
Edges
9
12
15
Edges
6
8
10
Vertices
6
8
10
Vertices
4
5
6
1.
Describe the pattern in the faces, edges, and vertices of the prisms.
2.
Describe the pattern in the faces, edges, and vertices of the pyramids.
3.
What is the relationship between the number of edges and vertices of any pyramid?
4.
Two of the faces of a prism are octagons, which have 8 sides. How many faces, edges,
and vertices does the prism have?
5.
One face of a pyramid is a decagon. A decagon has 10 sides. How many faces, edges,
and vertices does the prism have?
6.
Create Your Own On a separate sheet of paper, use the tables to make up a
pattern problem like problems 4 and 5. Solve the problem.
E–3
Name
Date
Pyramid and Prism Patterns
The tables show the number of faces, edges, and vertices of three different types of
prisms and pyramids. Use the tables to answer each question.
Prisms
Pyramids
Triangular
Rectangular
Pentagonal
Faces
5
6
7
Edges
9
12
Vertices
6
8
1.
Triangular
Rectangular
Pentagonal
Faces
4
5
6
15
Edges
6
8
10
10
Vertices
4
5
6
Describe the pattern in the faces, edges, and vertices of the prisms.
As the number of faces increases by 1, the number of
edges increases by 3, and the number of vertices
increases by 2.
2.
Describe the pattern in the faces, edges, and vertices of the pyramids.
As the number of faces increases by 1, the number of
edges increases by 2, and the number of vertices
increases by 1.
3.
What is the relationship between the number of edges and vertices of any pyramid?
They are the same.
4.
Two of the faces of a prism are octagons, which have 8 sides. How many faces, edges,
and vertices does the prism have?
10 faces, 24 edges, 16 vertices
5.
One face of a pyramid is a decagon. A decagon has 10 sides. How many faces, edges,
and vertices does the prism have?
11 faces, 20 edges, 11 vertices
6.
Create Your Own On a separate sheet of paper, use the tables to make up a
pattern problem like problems 4 and 5. Solve the problem. Answers will vary.