Unit 1, Lesson 13
Polyhedra
Grade 6
13.1
Warm-up
These five drawings represent polyhedra.
The next four drawings do not represent polyhedra.
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Your teacher will give you some figures or objects. Sort them into polyhedra and non-polyhedra.
- What characteristics helped you distinguish the polyhedra from the other figures?
13.2
Activity
- Here are some polyhedra called prisms.
A B C D E F Here are some polyhedra called pyramids.
P Q R S - Look at the prisms. What are their characteristics?
- Look at the pyramids. What are their characteristics?
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Which of these nets can be folded into Pyramid P? Select all that apply.
Three figures labeled net 1, net 2, and net 3. Net 1 has four small triangles arranged horizontally to create a parallelogram, net two has four small triangles arranged to make a larger triangle, and net 3 has four small triangles which all meet at their vertices. -
Your teacher will give your group some polygons and assign a polyhedron.
- Decide which polygons are needed to compose your assigned polyhedron. List the polygons and how many of each are needed.
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Arrange the cut-outs into a net that, if taped and folded, can be assembled into the polyhedron. Sketch the net. If possible, show a different net for the same polyhedron.
Student Lesson Summary
A polyhedron is a three-dimensional figure composed of faces. Each face is a polygon and meets only one other face along a complete edge. The ends of the edges meet at points that are called vertices.
A polyhedron always encloses a three-dimensional region.
The plural of polyhedron is polyhedra. Here are some drawings of polyhedra:
A prism is a type of polyhedron with two identical faces that are parallel to each other and that are called bases. The bases are connected by a set of rectangles (or sometimes parallelograms that aren’t rectangles).
A prism is named for the shape of its bases. For example, if the base is a pentagon, then it is called a “pentagonal prism.”
A pyramid is a type of polyhedron that has one special face called the base. All of the other faces are triangles that all meet at a single vertex.
A pyramid is named for the shape of its base. For example, if the base is a pentagon, then it is called a “pentagonal pyramid.”
A net is a two-dimensional representation of a polyhedron. It is composed of polygons that form the faces of a polyhedron.
A cube has 6 square faces, so its net is composed of six squares, as shown here.
A net can be cut out and folded to make a model of the polyhedron.
In a cube, every face shares its edges with 4 other squares. In a net of a cube, not all edges of the squares are joined with another edge. When the net is folded, each of these open edges will join another edge.
A base is a specific face of a prism or pyramid.
A prism has 2 identical bases that are parallel. A pyramid has 1 base.
A prism or pyramid is named for the shape of its base.
A net is a two-dimensional figure that can be folded to make a three-dimensional figure.
Here is a net for a cube.