How this calculation works
Calculate volume and area of a solid with twelve regular pentagonal faces.
THE FORMULA
V=(15+7√5)a³/4, A=3√(25+10√5)a²A worked example
An edge length of 2 gives volume 30+14√5.
Good to know
All faces must be regular pentagons of equal size.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Calculate volume and area of a solid with twelve regular pentagonal faces.
The primary result is labeled “Volume”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
All faces must be regular pentagons of equal size.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
An edge length of 2 gives volume 30+14√5.
Which rule does this calculator apply?
V=(15+7√5)a³/4, A=3√(25+10√5)a²