How do I find a square pyramid's volume?
One third of the base area times the height: a third of edge squared times height. Like a cone, a pyramid is a third of the box around it.
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Square Pyramid Volume Calculator
Find a square-based pyramid's volume, total surface area and slant height from its base edge and vertical height.
volume = ⅓a²h ; slant = √(h²+(a/2)²) ; surface = a² + 2a·slant
Frequently asked questions
What is the slant height?
The distance from the middle of a base edge up to the apex, along a triangular face. It is the square root of height squared plus half the base edge squared.
How is the surface area worked out?
The square base plus the four triangular faces: base edge squared plus two times base edge times slant height. The slant height sizes the triangles.
Why divide by three for the volume?
Because any pyramid fills exactly one third of the prism with the same base and height, a result that holds for all pyramids and cones alike.
Where is this seen?
The Egyptian pyramids, roof shapes, tent designs, and architectural spires with a square footprint.