## Space Diagonal of Dodecahedron given Face Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5)))))
dSpace = sqrt(3)*(1+sqrt(5))/2*sqrt((12*AFace)/(3*sqrt(25+(10*sqrt(5)))))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Space Diagonal of Dodecahedron - (Measured in Meter) - The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.
Face Area of Dodecahedron - (Measured in Square Meter) - The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Face Area of Dodecahedron: 175 Square Meter --> 175 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dSpace = sqrt(3)*(1+sqrt(5))/2*sqrt((12*AFace)/(3*sqrt(25+(10*sqrt(5))))) --> sqrt(3)*(1+sqrt(5))/2*sqrt((12*175)/(3*sqrt(25+(10*sqrt(5)))))
Evaluating ... ...
dSpace = 28.2645975327428
STEP 3: Convert Result to Output's Unit
28.2645975327428 Meter --> No Conversion Required
28.2645975327428 28.2646 Meter <-- Space Diagonal of Dodecahedron
(Calculation completed in 00.003 seconds)
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## < 12 Space Diagonal of Dodecahedron Calculators

Space Diagonal of Dodecahedron given Surface to Volume Ratio
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
Space Diagonal of Dodecahedron given Lateral Surface Area
Space Diagonal of Dodecahedron = (sqrt(3)*(1+sqrt(5)))/2*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
Space Diagonal of Dodecahedron given Total Surface Area
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Space Diagonal of Dodecahedron given Face Area
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5)))))
Space Diagonal of Dodecahedron given Insphere Radius
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
Space Diagonal of Dodecahedron given Volume
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Space Diagonal of Dodecahedron given Midsphere Radius
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5))
Space Diagonal of Dodecahedron given Face Perimeter
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Face Perimeter of Dodecahedron/10
Space Diagonal of Dodecahedron
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2
Space Diagonal of Dodecahedron given Perimeter
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Perimeter of Dodecahedron/60
Space Diagonal of Dodecahedron given Face Diagonal
Space Diagonal of Dodecahedron = sqrt(3)*Face Diagonal of Dodecahedron
Space Diagonal of Dodecahedron given Circumsphere Radius
Space Diagonal of Dodecahedron = 2*Circumsphere Radius of Dodecahedron

## Space Diagonal of Dodecahedron given Face Area Formula

Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5)))))
dSpace = sqrt(3)*(1+sqrt(5))/2*sqrt((12*AFace)/(3*sqrt(25+(10*sqrt(5)))))

## What is a Dodecahedron?

A Dodecahedron is a symmetric and closed three dimensional shape with 12 identical pentagonal faces. It is a Platonic solid, which has 12 faces, 20 vertices and 30 edges. At each vertex, three pentagonal faces meet and at each edge, two pentagonal faces meet. Out of all the five Platonic solids with identical edge length, Dodecahedron will have the highest value of volume and surface area.

## What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

## How to Calculate Space Diagonal of Dodecahedron given Face Area?

Space Diagonal of Dodecahedron given Face Area calculator uses Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5))))) to calculate the Space Diagonal of Dodecahedron, The Space Diagonal of Dodecahedron given Face Area formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using face area of Dodecahedron. Space Diagonal of Dodecahedron is denoted by dSpace symbol.

How to calculate Space Diagonal of Dodecahedron given Face Area using this online calculator? To use this online calculator for Space Diagonal of Dodecahedron given Face Area, enter Face Area of Dodecahedron (AFace) and hit the calculate button. Here is how the Space Diagonal of Dodecahedron given Face Area calculation can be explained with given input values -> 28.2646 = sqrt(3)*(1+sqrt(5))/2*sqrt((12*175)/(3*sqrt(25+(10*sqrt(5))))).

### FAQ

What is Space Diagonal of Dodecahedron given Face Area?
The Space Diagonal of Dodecahedron given Face Area formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using face area of Dodecahedron and is represented as dSpace = sqrt(3)*(1+sqrt(5))/2*sqrt((12*AFace)/(3*sqrt(25+(10*sqrt(5))))) or Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5))))). The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron.
How to calculate Space Diagonal of Dodecahedron given Face Area?
The Space Diagonal of Dodecahedron given Face Area formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using face area of Dodecahedron is calculated using Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5))))). To calculate Space Diagonal of Dodecahedron given Face Area, you need Face Area of Dodecahedron (AFace). With our tool, you need to enter the respective value for Face Area of Dodecahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Space Diagonal of Dodecahedron?
In this formula, Space Diagonal of Dodecahedron uses Face Area of Dodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
• Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2
• Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
• Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
• Space Diagonal of Dodecahedron = 2*Circumsphere Radius of Dodecahedron
• Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Face Perimeter of Dodecahedron/10
• Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
• Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5))
• Space Diagonal of Dodecahedron = sqrt(3)*Face Diagonal of Dodecahedron
• Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
• Space Diagonal of Dodecahedron = (sqrt(3)*(1+sqrt(5)))/2*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
• Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Perimeter of Dodecahedron/60
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