How this calculation works
Find volume and slant height from a regular base’s apothem.
THE FORMULA
Base area = n a² tan(π/n), volume = base area × height/3A worked example
A square with apothem 3 has area 36, giving volume 48 at height 4.
Good to know
The apex must be above the base centre.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find volume and slant height from a regular base’s apothem.
The primary result is labeled “Volume”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The apex must be above the base centre.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
A square with apothem 3 has area 36, giving volume 48 at height 4.
Which rule does this calculator apply?
Base area = n a² tan(π/n), volume = base area × height/3