Surface Area of Pyramids – Base Plus Triangular Faces
A pyramid's surface area splits into its base plus its lateral (triangular) faces. For a square pyramid with base side s and slant height l (the height measured along a triangular face, not straight up through the middle), each triangular face has area ½sl, and there are 4 of them, giving lateral area 2sl. Adding the square base: SA = s² + 2sl.
The slant height is the key measurement to watch for – it's easy to mix up with the pyramid's vertical height, but they measure different things: vertical height goes straight up to the apex, while slant height runs along the surface of a triangular face.
Calculating a Pyramid's Surface Area
For a square pyramid: SA = s² + 2sl, where s is the base side and l is the slant height (not the vertical height).
SA = 6² + 2(6)(10) = 36 + 120 = 156 cm².
Real-Life Application
- Tent design: calculating fabric for a pyramid-shaped tent.
- Roof cladding: the tiles or panels needed for a pyramid-shaped roof.
- Museum displays: glass panels for a pyramid-shaped structure, like the Louvre Pyramid.
Key Takeaways
- A square pyramid's surface area formula is SA = s² + 2sl.
- Slant height (along a triangular face) is different from vertical height.
- The lateral area alone (2sl) is a useful building block on its own.
Practice: Surface Area of Pyramids
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