Wentworth's Plane and Solid Geometry · Book VII, §§ 584–604 · Book 8: Book VII: Polyhedrons, Cylinders, and Cones

93. Polyhedrons, prisms and parallelopipeds

Goal: Your student can name and describe the common solids: polyhedrons, prisms (right, oblique, regular), parallelopipeds, cubes, and the unit of volume.

⏱ About 35 minutes · 6 steps

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You'll need

  • The book, open to these pages
  • A ruler (straightedge) and a pair of compasses
  • Sharp pencil, eraser and plain paper (or a geometry notebook)
  • Two or three stiff cards (to stand for planes) and a few pencils or straws (to stand for lines)
  • A few boxes and other flat-faced objects from around the house

What's in the book

The opening definitions of Book VII: polyhedrons and their names (§§ 584–588), prisms and parallelopipeds (§§ 589–599), volume (§§ 600–602), right sections and truncated prisms (§§ 603–604).

The lesson, step by step

  1. Warm up

    Ask: What is the sum of the face angles at a corner of a solid always less than? (Four right angles.)

  2. The new words

    Read §§ 584–588 together.

    A polyhedron is a solid bounded by planes.

    A prism is a polyhedron of which two faces are equal polygons in parallel planes, and the other faces are parallelograms.

    A parallelopiped is a prism whose bases are parallelograms.

  3. A solid hunt

    Gather a box, a die or sugar cube, a pencil with flat sides, and anything else with flat faces. For each, your student says whether it is a prism, whether it is right or oblique, and what its bases are. (A cereal box: a rectangular parallelopiped. A hexagonal pencil: a regular hexagonal prism.)

  4. Volume

    Read §§ 600–602.

    A cube whose edges are equal to the linear unit is taken as the unit of volume.

    Two solids are equivalent if their volumes are equal.

    Ask: How many unit cubes fit in a box 3 by 4 by 2? (24.)

  5. Drawing solids

    Read the note at § 588: full lines are visible edges, dashed lines hidden ones. Your student draws a triangular prism and a cube this way.

  6. Wrap up

    Your student copies the definitions of prism, right prism, regular prism, parallelopiped and cube into the notebook, each with a small sketch.

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