# Dodecahedron

From PreparingYou

What is the mathematical formula used to determine the area inside a pentadodecahedron?

A penta-dodecahedron is the same as a Dodecahedron which has twelve faces consisting of equal pentagon surfaces. The volume of a Dodecahedron, if the length of one side of a pentagon is equal to "a", will be close to 1 ⁄ 4 × (15 + 7 × √5) × a³ ≈ 7.663118961 × a³ Since 7.663118961 is an approximate number and the square root of 5 is approximately 2.236 this formula can only be close

Where the Volume=V and the length of the side of a pentagon = a the formula is

- V = 1 ⁄ 4 × (15 + 7 × √5) × a³ ≈ 7.663118961 × a³