## Face Area of Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
AFace = 1/4*sqrt(25+(10*sqrt(5)))*((4*rm)/(3+sqrt(5)))^2
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 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.
Midsphere Radius of Dodecahedron - (Measured in Meter) - The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Dodecahedron: 13 Meter --> 13 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
AFace = 1/4*sqrt(25+(10*sqrt(5)))*((4*rm)/(3+sqrt(5)))^2 --> 1/4*sqrt(25+(10*sqrt(5)))*((4*13)/(3+sqrt(5)))^2
Evaluating ... ...
AFace = 169.685646423862
STEP 3: Convert Result to Output's Unit
169.685646423862 Square Meter --> No Conversion Required
169.685646423862 169.6856 Square Meter <-- Face Area of Dodecahedron
(Calculation completed in 00.004 seconds)
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## < 12 Face Area of Dodecahedron Calculators

Face Area of Dodecahedron given Surface to Volume Ratio
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
Face Area of Dodecahedron given Insphere Radius
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2
Face Area of Dodecahedron given Circumsphere Radius
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Face Area of Dodecahedron given Space Diagonal
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Face Area of Dodecahedron given Midsphere Radius
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
Face Area of Dodecahedron given Volume
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
Face Area of Dodecahedron given Face Diagonal
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
Face Area of Dodecahedron given Face Perimeter
Face Area of Dodecahedron = 1/100*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
Face Area of Dodecahedron given Perimeter
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*(Perimeter of Dodecahedron/30)^2
Face Area of Dodecahedron
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Face Area of Dodecahedron given Lateral Surface Area
Face Area of Dodecahedron = Lateral Surface Area of Dodecahedron/10
Face Area of Dodecahedron given Total Surface Area
Face Area of Dodecahedron = Total Surface Area of Dodecahedron/12

## < 8 Area of Dodecahedron Calculators

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

## Face Area of Dodecahedron given Midsphere Radius Formula

Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
AFace = 1/4*sqrt(25+(10*sqrt(5)))*((4*rm)/(3+sqrt(5)))^2

## 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 Area of Dodecahedron given Midsphere Radius?

Face Area of Dodecahedron given Midsphere Radius calculator uses Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2 to calculate the Face Area of Dodecahedron, The Face Area of Dodecahedron given Midsphere Radius formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using midsphere radius of Dodecahedron. Face Area of Dodecahedron is denoted by AFace symbol.

How to calculate Face Area of Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Face Area of Dodecahedron given Midsphere Radius, enter Midsphere Radius of Dodecahedron (rm) and hit the calculate button. Here is how the Face Area of Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 169.6856 = 1/4*sqrt(25+(10*sqrt(5)))*((4*13)/(3+sqrt(5)))^2.

### FAQ

What is Face Area of Dodecahedron given Midsphere Radius?
The Face Area of Dodecahedron given Midsphere Radius formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using midsphere radius of Dodecahedron and is represented as AFace = 1/4*sqrt(25+(10*sqrt(5)))*((4*rm)/(3+sqrt(5)))^2 or Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2. The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.
How to calculate Face Area of Dodecahedron given Midsphere Radius?
The Face Area of Dodecahedron given Midsphere Radius formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using midsphere radius of Dodecahedron is calculated using Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2. To calculate Face Area of Dodecahedron given Midsphere Radius, you need Midsphere Radius of Dodecahedron (rm). With our tool, you need to enter the respective value for Midsphere Radius 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 Area of Dodecahedron?
In this formula, Face Area of Dodecahedron uses Midsphere Radius of Dodecahedron. We can use 12 other way(s) to calculate the same, which is/are as follows -
• Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
• Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
• Face Area of Dodecahedron = Total Surface Area of Dodecahedron/12
• Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
• Face Area of Dodecahedron = 1/100*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
• Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2
• Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
• Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
• Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
• Face Area of Dodecahedron = Lateral Surface Area of Dodecahedron/10
• Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*(Perimeter of Dodecahedron/30)^2
• Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
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