Pyramids and Prisms in Geometry
Pyramids
What do they all have in common?
Pyramids
Definition
A solid object where:
• The base is a
polygon
(a straight-
sided flat shape)
• The sides are triangles which meet at
the top (the
apex
).
Prisms
What do they all have in common?
Prisms
Definition
A solid object with two identical ends
and flat sides:
• The sides are rectangles (or
parallelograms)
• The
cross section
is the same all
along its length
The shape of the ends give the prism a
name, such as "triangular prism"
face
edge
vertex (plural vertices)
Pyramids
Fill in the table for each of the pyramids
Can you find a predict the results for a heptagonal or octagonal
based pyramid? What about an n-agonal based pyramid?
Pyramids
Fill in the table for each of the pyramids
Can you find a connection between the
F
aces,
E
dges and
V
ertices?
Euler’s Formula for Polyhedra
V + F - E = 2.
The formula was discovered by
and bears the name of the
famous Swiss mathematician
Leonhard Euler
(1707 - 1783)
It is true for all
polyhedra.
(singular –
polyhedron
)
Prisms
Fill in the table for each of the prisms
Can you find a predict the results for a heptagonal or octagonal
prism? What about an n-agonal prism?
Prisms
Fill in the table for each of the prisms
Verify that Euler’s formula also works for the prisms in this table
Other Polyhedra
Fill in the table for each of these
platonic solids
How can you use Euler’s formula to fill in this table?
Octahedron
Icosahedron
Dodecahedron
Why are there only 5 platonic solids?
Explore the common characteristics of pyramids and prisms, learn about their definitions, faces, edges, and vertices, and understand Euler's formula for polyhedra. Discover the properties of different pyramids and prisms and predict results based on various base shapes. Verify Euler's formula for prisms and delve into the fascinating world of geometrical solids.
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Presentation Transcript
Pyramids What do they all have in common?
Pyramids Definition A solid object where: The base is a polygon (a straight- sided flat shape) The sides are triangles which meet at the top (the apex).
Prisms What do they all have in common?
Prisms Definition A solid object with two identical ends and flat sides: The sides are rectangles (or parallelograms) The cross section is the same all along its length The shape of the ends give the prism a name, such as "triangular prism"
Pyramids Fill in the table for each of the pyramids Solid Number of Faces Number of Edges Number of Vertices Can you find a predict the results for a heptagonal or octagonal based pyramid? What about an n-agonal based pyramid?
Pyramids Fill in the table for each of the pyramids Solid Number of Faces Number of Edges Number of Vertices Can you find a connection between the Faces, Edges and Vertices?
Eulers Formula for Polyhedra V + F - E = 2. The formula was discovered by and bears the name of the famous Swiss mathematician Leonhard Euler (1707 - 1783) It is true for all polyhedra. (singular polyhedron)
Prisms Fill in the table for each of the prisms Solid Number of Faces Number of Edges Number of Vertices Can you find a predict the results for a heptagonal or octagonal prism? What about an n-agonal prism?
Prisms Fill in the table for each of the prisms Solid Number of Faces Number of Edges Number of Vertices Verify that Euler s formula also works for the prisms in this table
Other Polyhedra Fill in the table for each of these platonic solids Solid Number of Faces Number of Edges Number of Vertices Octahedron Dodecahedron Icosahedron How can you use Euler s formula to fill in this table?
