Prisms – Solids with a Uniform Cross-Section
A prism is a solid with two identical, parallel end faces (called bases), connected by rectangular side faces. The key feature of a prism is that its cross-section – the shape you'd see if you sliced straight through it, parallel to the bases – is exactly the same all the way along its length. A prism is always named after the shape of its base: a triangular prism has triangular bases, a pentagonal prism has pentagonal bases, and so on.
Cuboids and cubes are actually both special types of prism – a cuboid is a “rectangular prism,” with a rectangle as its cross-section. Once you can count the faces, edges, and vertices of a prism from its base shape, you can predict these counts for a prism with any number of sides.
Naming and Counting Prisms
A prism with an n-sided cross-section has (n + 2) faces, (2n) vertices, and (3n) edges. It is named after its cross-section shape.
A hexagon has 6 sides: faces = 6 + 2 = 8 (2 hexagonal ends plus 6 rectangular sides).
Real-Life Application
- Pencils: many pencils are hexagonal prisms.
- Toblerone bars: a classic real-world triangular prism.
- Prism (optics): a glass triangular prism splits white light into a rainbow.
Key Takeaways
- A prism has a uniform cross-section along its entire length.
- It is named after the shape of its cross-section (e.g. triangular prism).
- Cubes and cuboids are special prisms with a square or rectangular cross-section.
Practice: Prisms
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