## Face Area of Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Area of Icosahedron = sqrt(3)/4*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
AFace = sqrt(3)/4*((12*ri)/(sqrt(3)*(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 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.
Insphere Radius of Icosahedron - (Measured in Meter) - Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.
STEP 1: Convert Input(s) to Base Unit
Insphere Radius of Icosahedron: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
AFace = sqrt(3)/4*((12*ri)/(sqrt(3)*(3+sqrt(5))))^2 --> sqrt(3)/4*((12*7)/(sqrt(3)*(3+sqrt(5))))^2
Evaluating ... ...
AFace = 37.1473126554519
STEP 3: Convert Result to Output's Unit
37.1473126554519 Square Meter --> No Conversion Required
FINAL ANSWER
37.1473126554519 37.14731 Square Meter <-- Face Area of Icosahedron
(Calculation completed in 00.004 seconds)
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Created by Dhruv Walia
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

## Face Area of Icosahedron given Insphere Radius Formula

Face Area of Icosahedron = sqrt(3)/4*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
AFace = sqrt(3)/4*((12*ri)/(sqrt(3)*(3+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 Insphere Radius?

Face Area of Icosahedron given Insphere Radius calculator uses Face Area of Icosahedron = sqrt(3)/4*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2 to calculate the Face Area of Icosahedron, The Face Area of Icosahedron given Insphere 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 insphere radius of the Icosahedron. Face Area of Icosahedron is denoted by AFace symbol.

How to calculate Face Area of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Face Area of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (ri) and hit the calculate button. Here is how the Face Area of Icosahedron given Insphere Radius calculation can be explained with given input values -> 37.14731 = sqrt(3)/4*((12*7)/(sqrt(3)*(3+sqrt(5))))^2.

### FAQ

What is Face Area of Icosahedron given Insphere Radius?
The Face Area of Icosahedron given Insphere 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 insphere radius of the Icosahedron and is represented as AFace = sqrt(3)/4*((12*ri)/(sqrt(3)*(3+sqrt(5))))^2 or Face Area of Icosahedron = sqrt(3)/4*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2. Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.
How to calculate Face Area of Icosahedron given Insphere Radius?
The Face Area of Icosahedron given Insphere 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 insphere radius of the Icosahedron is calculated using Face Area of Icosahedron = sqrt(3)/4*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2. To calculate Face Area of Icosahedron given Insphere Radius, you need Insphere Radius of Icosahedron (ri). With our tool, you need to enter the respective value for Insphere 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 Insphere Radius of Icosahedron. We can use 11 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*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*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
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