Slicing Prisms and Pyramids
Think about this box. This box has many faces,
vertices, and edges, many of which can't be
seen in this picture.
How many faces does this box have?
How many vertices does this box have?
How many edges does this box have?
Today we're going to talk about strategies for carving polygonal prisms
out of rectangular prisms.
Consider this square prism. How could we cut this prism into a
triangular prism?
A pentagonal prism?
A hexagonal prism?
Slicing Prisms and Pyramids
Some interesting shapes result when you cut prisms from different
angles. Suppose that you start with a rectangular prism and make one
cut in the directions indicated by the dashed lines. In your groups,
answer the following questions for each prism.
• What are the shapes of the two resulting figures?
• What are the shapes of the faces of the figures?
• How many vertices, edges, and faces does each figure have?
1.
2.
3.
side view
front view
front view
side view
A pyramid is a solid figure with a
polygonal base and triangular faces
that rise to a common vertex.
Suppose we had a cube. How could we
make cuts in the cube to produce a
pyramid with one side of the cube as the
base?
Suppose we had a cube. How could we
make cuts in the cube to produce a pyramid
with a triangle as the base (triangular
pyramid)?