Square Pyramid Volume and Surface Area
The volume of a pyramid formula for a square base is V = ⅓a²h: one third of the box it fits inside.
3D Solids
Square Pyramid
A square pyramid has a square base and four triangular faces meeting at the apex. Its volume is one third of the matching prism.
- Volume
- V = (1 ⁄ 3) a2h
- Slant height
- s = √(h2 + (a ⁄ 2)2)
- Surface area
- SA = a2 + 2as
- a base edge
- h height
- s slant height
Example 1: volume
A square pyramid has a base of 6 cm and a height of 4 cm.
- V = ⅓ × a² × h
- V = ⅓ × 6² × 4 = ⅓ × 144
- V = 48 cm³
Example 2: slant height
The slant height l runs from the tip to the middle of a base edge. It is the hypotenuse of a right triangle with legs h and a ⁄ 2.
- l = √(4² + 3²) = √25 = 5 cm
Example 3: surface area
- Base = 6² = 36 cm²
- Four triangles = 4 × ½ × 6 × 5 = 60 cm²
- Total = 36 + 60 = 96 cm²
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Try it yourself
The Great Pyramid had a base of about 230 m and a height of about 147 m. Estimate its volume.
Show the answer
V = ⅓ × 230² × 147 ≈ 2,592,100 m³
More on the square pyramid formulas page.
Square pyramid: FAQ
What is the volume of a square pyramid?
V = ⅓a²h, where a is the base side and h is the vertical height.
What is the slant height?
The height of each triangular face: l = √(h² + (a ⁄ 2)²).
What is the surface area of a square pyramid?
SA = a² + 2al: the base plus four triangles.