How it’s calculated
Any pyramid holds one third of the prism with the same base and height. For a right rectangular pyramid, each pair of opposite triangular faces has its own slant height.
Example: a 6 ft × 6 ft base with height 4 ft gives V = (1/3) × 36 × 4 = 48 ft³. Both slant heights are √(9 + 16) = 5 ft, so the lateral area is 6 × 5 + 6 × 5 = 60 ft² and the total is 96 ft².
Frequently asked questions
What is the volume formula for a pyramid?
V = ⅓ × base area × height. For a rectangular base, that is ⅓ × L × W × H.
What about a triangular or hexagonal pyramid?
The same rule applies: one third of the base area times the height. Find the base area with the triangle or polygon calculator.
Is the height the same as the slant height?
No. Height is measured straight up from the base centre to the apex; slant height runs along a face and is always longer.
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Sources
- Pyramid — Wolfram MathWorld
- Square Pyramid — Wolfram MathWorld
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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