Face Area of Icosahedron given Space Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
AFace = sqrt(3)/4*((2*dSpace)/(sqrt(10+(2*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.
Space Diagonal of Icosahedron - (Measured in Meter) - The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Space Diagonal of Icosahedron: 19 Meter --> 19 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
AFace = sqrt(3)/4*((2*dSpace)/(sqrt(10+(2*sqrt(5)))))^2 --> sqrt(3)/4*((2*19)/(sqrt(10+(2*sqrt(5)))))^2
Evaluating ... ...
AFace = 43.2051179920237
STEP 3: Convert Result to Output's Unit
43.2051179920237 Square Meter --> No Conversion Required
FINAL ANSWER
43.2051179920237 43.20512 Square Meter <-- Face Area of Icosahedron
(Calculation completed in 00.004 seconds)

Credits

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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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Mumbai University (DJSCE), Mumbai
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12 Face Area of Icosahedron Calculators

Face Area of Icosahedron given Surface to Volume Ratio
​ Go 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
​ Go 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
​ Go 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
​ Go 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
​ Go Face Area of Icosahedron = sqrt(3)/4*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
Face Area of Icosahedron given Volume
​ Go 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
​ Go Face Area of Icosahedron = (Total Surface Area of Icosahedron-Lateral Surface Area of Icosahedron)/2
Face Area of Icosahedron given Face Perimeter
​ Go Face Area of Icosahedron = sqrt(3)/4*(Face Perimeter of Icosahedron/3)^2
Face Area of Icosahedron given Perimeter
​ Go Face Area of Icosahedron = sqrt(3)/4*(Perimeter of Icosahedron/30)^2
Face Area of Icosahedron
​ Go Face Area of Icosahedron = sqrt(3)/4*Edge Length of Icosahedron^2
Face Area of Icosahedron given Lateral Surface Area
​ Go Face Area of Icosahedron = Lateral Surface Area of Icosahedron/18
Face Area of Icosahedron given Total Surface Area
​ Go Face Area of Icosahedron = Total Surface Area of Icosahedron/20

Face Area of Icosahedron given Space Diagonal Formula

Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
AFace = sqrt(3)/4*((2*dSpace)/(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 Space Diagonal?

Face Area of Icosahedron given Space Diagonal calculator uses Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2 to calculate the Face Area of Icosahedron, The Face Area of Icosahedron given Space Diagonal 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 space diagonal of the Icosahedron. Face Area of Icosahedron is denoted by AFace symbol.

How to calculate Face Area of Icosahedron given Space Diagonal using this online calculator? To use this online calculator for Face Area of Icosahedron given Space Diagonal, enter Space Diagonal of Icosahedron (dSpace) and hit the calculate button. Here is how the Face Area of Icosahedron given Space Diagonal calculation can be explained with given input values -> 43.20512 = sqrt(3)/4*((2*19)/(sqrt(10+(2*sqrt(5)))))^2.

FAQ

What is Face Area of Icosahedron given Space Diagonal?
The Face Area of Icosahedron given Space Diagonal 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 space diagonal of the Icosahedron and is represented as AFace = sqrt(3)/4*((2*dSpace)/(sqrt(10+(2*sqrt(5)))))^2 or Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. The Space Diagonal of Icosahedron is the line connecting two vertices that are not on the same face of Icosahedron.
How to calculate Face Area of Icosahedron given Space Diagonal?
The Face Area of Icosahedron given Space Diagonal 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 space diagonal of the Icosahedron is calculated using Face Area of Icosahedron = sqrt(3)/4*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. To calculate Face Area of Icosahedron given Space Diagonal, you need Space Diagonal of Icosahedron (dSpace). With our tool, you need to enter the respective value for Space Diagonal 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 Space Diagonal 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*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+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*(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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