IM 1
Investigation 5.1.1A
Name
Polyhedron: A geometric solid (3-Dimensional Shape) with flat faces and straight edges.
Prism: A Polyhedron with 2 parallel bases that are polygons, and sides that are rectangles.
Pyramid: A Polyhedron with a single base that is a polygon, and sides that are triangles.
B
C
E
A
F
D
G
I
L
J
H
K
1) Which of the shapes shown above can be considered prisms?
2) Which of the shapes shown above can be considered pyramids?
3) Which of the shapes shown above are not prisms or pyramids?
4) Prisms and pyramids are named by the shape of their base. For example a prism with a rectangle base would
be called a rectangular prism, and a pyramid with a triangle base would be called a triangular pyramid. Name
each of the shapes shown above. Also try to name the shapes that are not prisms or pyramids.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
5)
How is a Cone similar to a Pyramid?
How is a Cone different from a Pyramid?
How is a Cylinder similar to a Prism?
How is a Cylinder different from a Prism?
Face: The sides and bases of a prism or pyramid are called
faces. The faces are the polygons that form the
surface of the shape.
Vertex
Edge: The lines where two polygons meet on a prism or
pyramid are called edges.
Vertex: The point or corner where 3 or more polygons meet
on a prism or pyramid are called vertices.
Face
Edge
6) For each of the following prisms count the number of Faces, Edges, and Vertices. Refer back to the pictures
on the previous side to help you count them up. Using the pattern that you notice calculate the answers for
the shapes that were not drawn.
7) Write an equation to calculate the number of faces for any prism using the variable N = number of sides on a
base, and F = number of faces.
8) Write an equation to calculate the number of edges for any prism using the variable N = number of sides on a
base, and E = number of edges.
9) Write an equation to calculate the number of vertices for any prism using the variable N = number of sides
on a base, and V = number of vertices.
10) How many faces, edges, and vertices would a prism have if it were made with 15 sides on its base?
Faces:
Edges:
Vertices:
11) For each of the following pyramids count the number of Faces, Edges, and Vertices. Refer back to the
pictures on the previous side to help you count them up. Using the pattern that you notice calculate the
answers for the shapes that were not drawn.
12) Write an equation to calculate the number of faces for any pyramid using the variable N = number of sides
on a base, and F = number of faces.
13) Write an equation to calculate the number of edges for any pyramid using the variable N = number of sides
on a base, and E = number of edges.
14) Write an equation to calculate the number of vertices for any pyramid using the variable N = number of
sides on a base, and V = number of vertices.
15) How many faces, edges, and vertices would a pyramid have if it were made with 15 sides on its base?
Faces:
Edges:
Vertices:
16) Name a shape that you see in your home, daily life, or around the world that can be considered each of the
5 shapes below. Give at least one example of each, but try for more.
Prism:
Pyramid:
Cylinder:
Cone:
Sphere:
EC: Find pictures of real-life versions of these shapes in a magazine or take pictures of objects you see around
you house. Write an explanation of what each picture is including the name of the shape. For credit you
must have at least 8 different objects, and there must be at least one of each of the following: (prism,
pyramid, cone, cylinder, and sphere.) You can turn this in on paper or email me the explanation with the
pictures as attachments at [email protected]