Face Diagonal of Dodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
dFace = (1+sqrt(5))/2*sqrt(TSA/(3*sqrt(25+(10*sqrt(5)))))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Face Diagonal of Dodecahedron - (Measured in Meter) - The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.
Total Surface Area of Dodecahedron - (Measured in Square Meter) - Total Surface Area of Dodecahedron is the total quantity of plane enclosed by the entire surface of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Total Surface Area of Dodecahedron: 2100 Square Meter --> 2100 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dFace = (1+sqrt(5))/2*sqrt(TSA/(3*sqrt(25+(10*sqrt(5))))) --> (1+sqrt(5))/2*sqrt(2100/(3*sqrt(25+(10*sqrt(5)))))
Evaluating ... ...
dFace = 16.3185729940655
STEP 3: Convert Result to Output's Unit
16.3185729940655 Meter --> No Conversion Required
FINAL ANSWER
16.3185729940655 16.31857 Meter <-- Face Diagonal of Dodecahedron
(Calculation completed in 00.020 seconds)

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Face Diagonal of Dodecahedron Calculators

Face Diagonal of Dodecahedron given Total Surface Area
​ LaTeX ​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Face Area
​ LaTeX ​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Volume
​ LaTeX ​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Face Diagonal of Dodecahedron
​ LaTeX ​ Go Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron

Diagonal of Dodecahedron Calculators

Face Diagonal of Dodecahedron given Total Surface Area
​ LaTeX ​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Insphere Radius
​ LaTeX ​ Go Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
Space Diagonal of Dodecahedron
​ LaTeX ​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2
Face Diagonal of Dodecahedron
​ LaTeX ​ Go Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron

Face Diagonal of Dodecahedron given Total Surface Area Formula

​LaTeX ​Go
Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
dFace = (1+sqrt(5))/2*sqrt(TSA/(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 Face Diagonal of Dodecahedron given Total Surface Area?

Face Diagonal of Dodecahedron given Total Surface Area calculator uses Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5))))) to calculate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron given Total Surface Area formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using total surface area of Dodecahedron. Face Diagonal of Dodecahedron is denoted by dFace symbol.

How to calculate Face Diagonal of Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Face Diagonal of Dodecahedron given Total Surface Area, enter Total Surface Area of Dodecahedron (TSA) and hit the calculate button. Here is how the Face Diagonal of Dodecahedron given Total Surface Area calculation can be explained with given input values -> 16.31857 = (1+sqrt(5))/2*sqrt(2100/(3*sqrt(25+(10*sqrt(5))))).

FAQ

What is Face Diagonal of Dodecahedron given Total Surface Area?
The Face Diagonal of Dodecahedron given Total Surface Area formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using total surface area of Dodecahedron and is represented as dFace = (1+sqrt(5))/2*sqrt(TSA/(3*sqrt(25+(10*sqrt(5))))) or Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5))))). Total Surface Area of Dodecahedron is the total quantity of plane enclosed by the entire surface of the Dodecahedron.
How to calculate Face Diagonal of Dodecahedron given Total Surface Area?
The Face Diagonal of Dodecahedron given Total Surface Area formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using total surface area of Dodecahedron is calculated using Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5))))). To calculate Face Diagonal of Dodecahedron given Total Surface Area, you need Total Surface Area of Dodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface 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 Face Diagonal of Dodecahedron?
In this formula, Face Diagonal of Dodecahedron uses Total Surface Area of Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron
  • Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
  • Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))
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