Formula and example
How it is calculated
V=h(a²+ab+b²)/3; s=√[h²+((a−b)/2)²]; L=2(a+b)s; S=a²+b²+L.
Worked example
With a=6 cm, b=3 cm and h=4 cm, the volume is 4(36+18+9)/3 = 84 cm³.
Things to check
- The squares have the same orientation and a shared central axis. Rotated or offset faces are not covered.
- b=0 gives a complete square pyramid; b=a gives a square prism.
Frequently asked questions
Can I just average the areas of the two bases?
That generally gives the wrong volume. The geometrical relationship also includes ab, the square root of the product of the base areas.