## Face Area of Icosahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
AFace = sqrt(3)/4*((4*rc)/(sqrt(10+(2*sqrt(5)))))^2
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Face Area of Icosahedron - (Measured in Square Meter) - The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.
Circumsphere Radius of Icosahedron - (Measured in Meter) - Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.
STEP 1: Convert Input(s) to Base Unit
Circumsphere Radius of Icosahedron: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
AFace = sqrt(3)/4*((4*rc)/(sqrt(10+(2*sqrt(5)))))^2 --> sqrt(3)/4*((4*9)/(sqrt(10+(2*sqrt(5)))))^2
Evaluating ... ...
AFace = 38.7768926022595
STEP 3: Convert Result to Output's Unit
38.7768926022595 Square Meter --> No Conversion Required
38.7768926022595 38.77689 Square Meter <-- Face Area of Icosahedron
(Calculation completed in 00.004 seconds)
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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 12 Face Area of Icosahedron Calculators

Face Area of Icosahedron given Surface to Volume Ratio
Face Area of Icosahedron = sqrt(3)/4*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^2
Face Area of Icosahedron given Circumsphere Radius
Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Face Area of Icosahedron given Insphere Radius
Face Area of Icosahedron = sqrt(3)/4*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
Face Area of Icosahedron given Space Diagonal
Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Face Area of Icosahedron given Midsphere Radius
Face Area of Icosahedron = sqrt(3)/4*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
Face Area of Icosahedron given Volume
Face Area of Icosahedron = sqrt(3)/4*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(2/3)
Face Area of Icosahedron given Total Surface Area and Lateral Surface Area
Face Area of Icosahedron = (Total Surface Area of Icosahedron-Lateral Surface Area of Icosahedron)/2
Face Area of Icosahedron given Face Perimeter
Face Area of Icosahedron = sqrt(3)/4*(Face Perimeter of Icosahedron/3)^2
Face Area of Icosahedron given Perimeter
Face Area of Icosahedron = sqrt(3)/4*(Perimeter of Icosahedron/30)^2
Face Area of Icosahedron
Face Area of Icosahedron = sqrt(3)/4*Edge Length of Icosahedron^2
Face Area of Icosahedron given Lateral Surface Area
Face Area of Icosahedron = Lateral Surface Area of Icosahedron/18
Face Area of Icosahedron given Total Surface Area
Face Area of Icosahedron = Total Surface Area of Icosahedron/20

## < 10+ Surface Area of Icosahedron Calculators

Total Surface Area of Icosahedron given Circumsphere Radius
Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Face Area of Icosahedron given Circumsphere Radius
Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length
Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2
Lateral Surface Area of Icosahedron given Volume
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(2/3)
Total Surface Area of Icosahedron given Volume
Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(2/3)
Lateral Surface Area of Icosahedron
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*Edge Length of Icosahedron^2
Total Surface Area of Icosahedron
Total Surface Area of Icosahedron = 5*sqrt(3)*Edge Length of Icosahedron^2
Face Area of Icosahedron
Face Area of Icosahedron = sqrt(3)/4*Edge Length of Icosahedron^2
Lateral Surface Area of Icosahedron given Total Surface Area
Lateral Surface Area of Icosahedron = 9/10*Total Surface Area of Icosahedron
Face Area of Icosahedron given Total Surface Area
Face Area of Icosahedron = Total Surface Area of Icosahedron/20

## Face Area of Icosahedron given Circumsphere Radius Formula

Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
AFace = sqrt(3)/4*((4*rc)/(sqrt(10+(2*sqrt(5)))))^2

## What is an Icosahedron?

An Icosahedron is a symmetric and closed three dimensional shape with 20 identical equilateral triangular faces. It is a Platonic solid, which has 20 faces, 12 vertices and 30 edges. At each vertex, five equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

## 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 Icosahedron given Circumsphere Radius?

Face Area of Icosahedron given Circumsphere Radius calculator uses Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2 to calculate the Face Area of Icosahedron, The Face Area of Icosahedron given Circumsphere Radius formula is defined as the amount of space occupied on any one of the twelve triangular faces of an Icosahedron and is calculated using the circumsphere radius of the Icosahedron. Face Area of Icosahedron is denoted by AFace symbol.

How to calculate Face Area of Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Face Area of Icosahedron given Circumsphere Radius, enter Circumsphere Radius of Icosahedron (rc) and hit the calculate button. Here is how the Face Area of Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 38.77689 = sqrt(3)/4*((4*9)/(sqrt(10+(2*sqrt(5)))))^2.

### FAQ

What is Face Area of Icosahedron given Circumsphere Radius?
The Face Area of Icosahedron given Circumsphere Radius formula is defined as the amount of space occupied on any one of the twelve triangular faces of an Icosahedron and is calculated using the circumsphere radius of the Icosahedron and is represented as AFace = sqrt(3)/4*((4*rc)/(sqrt(10+(2*sqrt(5)))))^2 or Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.
How to calculate Face Area of Icosahedron given Circumsphere Radius?
The Face Area of Icosahedron given Circumsphere Radius formula is defined as the amount of space occupied on any one of the twelve triangular faces of an Icosahedron and is calculated using the circumsphere radius of the Icosahedron is calculated using Face Area of Icosahedron = sqrt(3)/4*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. To calculate Face Area of Icosahedron given Circumsphere Radius, you need Circumsphere Radius of Icosahedron (rc). With our tool, you need to enter the respective value for Circumsphere Radius of Icosahedron 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 Icosahedron?
In this formula, Face Area of Icosahedron uses Circumsphere Radius of Icosahedron. We can use 13 other way(s) to calculate the same, which is/are as follows -
• Face Area of Icosahedron = sqrt(3)/4*Edge Length of Icosahedron^2
• Face Area of Icosahedron = sqrt(3)/4*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
• Face Area of Icosahedron = sqrt(3)/4*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
• Face Area of Icosahedron = sqrt(3)/4*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^2
• Face Area of Icosahedron = Total Surface Area of Icosahedron/20
• Face Area of Icosahedron = sqrt(3)/4*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(2/3)
• Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
• Face Area of Icosahedron = sqrt(3)/4*(Face Perimeter of Icosahedron/3)^2
• Face Area of Icosahedron = Lateral Surface Area of Icosahedron/18
• Face Area of Icosahedron = (Total Surface Area of Icosahedron-Lateral Surface Area of Icosahedron)/2
• Face Area of Icosahedron = sqrt(3)/4*(Perimeter of Icosahedron/30)^2
• Face Area of Icosahedron = sqrt(3)/4*Edge Length of Icosahedron^2
• Face Area of Icosahedron = Total Surface Area of Icosahedron/20
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