Pyramids – Solids That Taper to an Apex
A pyramid is a solid with one polygon base and triangular side faces that all meet at a single top point, called the apex. Unlike a prism, a pyramid's cross-section shrinks as you move up toward the apex, rather than staying the same size. Like prisms, pyramids are named after the shape of their base – a square pyramid has a square base, a triangular pyramid has a triangular base, and so on.
The most famous pyramids in the world – the Great Pyramid of Giza and its neighbours in Egypt – are square pyramids, built more than 4,500 years ago. Their four triangular faces rise from a square base to meet at a single apex, exactly matching the mathematical definition still used today.
Naming and Counting Pyramids
A pyramid with an n-sided base has (n + 1) faces, (n + 1) vertices, and (2n) edges. It is named after its base shape.
A square has 4 sides: faces = 4 + 1 = 5 (1 square base plus 4 triangular sides).
Real-Life Application
- The Egyptian pyramids: the most famous real-world square pyramids.
- Tents: many camping tents are shaped like pyramids.
- Roof designs: some hip roofs form a pyramid shape.
Key Takeaways
- A pyramid tapers from a polygon base to a single apex.
- It is named after the shape of its base (e.g. square pyramid).
- The Egyptian pyramids are real-world square pyramids over 4,500 years old.
Practice: Pyramids
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