## Lateral Surface Area of Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
LSA = 9*sqrt(3)/2*((12*ri)/(sqrt(3)*(3+sqrt(5))))^2
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Lateral Surface Area of Icosahedron - (Measured in Square Meter) - Lateral Surface Area of Icosahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the 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
LSA = 9*sqrt(3)/2*((12*ri)/(sqrt(3)*(3+sqrt(5))))^2 --> 9*sqrt(3)/2*((12*7)/(sqrt(3)*(3+sqrt(5))))^2
Evaluating ... ...
LSA = 668.651627798135
STEP 3: Convert Result to Output's Unit
668.651627798135 Square Meter --> No Conversion Required
668.651627798135 668.6516 Square Meter <-- Lateral Surface Area of Icosahedron
(Calculation completed in 00.003 seconds)
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## < 12 Lateral Surface Area of Icosahedron Calculators

Lateral Surface Area of Icosahedron given Surface to Volume Ratio
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^2
Lateral Surface Area of Icosahedron given Circumsphere Radius
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Lateral Surface Area of Icosahedron given Insphere Radius
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
Lateral Surface Area of Icosahedron given Space Diagonal
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Lateral Surface Area of Icosahedron given Total Surface Area and Edge Length
Lateral Surface Area of Icosahedron = Total Surface Area of Icosahedron-sqrt(3)/2*Edge Length of Icosahedron^2
Lateral Surface Area of Icosahedron given Midsphere Radius
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^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)
Lateral Surface Area of Icosahedron given Face Perimeter
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Face Perimeter of Icosahedron/3)^2
Lateral Surface Area of Icosahedron given Perimeter
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Perimeter of Icosahedron/30)^2
Lateral Surface Area of Icosahedron
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*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
Lateral Surface Area of Icosahedron given Face Area
Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron

## Lateral Surface Area of Icosahedron given Insphere Radius Formula

Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
LSA = 9*sqrt(3)/2*((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 Lateral Surface Area of Icosahedron given Insphere Radius?

Lateral Surface Area of Icosahedron given Insphere Radius calculator uses Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2 to calculate the Lateral Surface Area of Icosahedron, The Lateral Surface Area of Icosahedron given Insphere Radius formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron and is calculated using the insphere radius of the Icosahedron. Lateral Surface Area of Icosahedron is denoted by LSA symbol.

How to calculate Lateral Surface Area of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Lateral Surface Area of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (ri) and hit the calculate button. Here is how the Lateral Surface Area of Icosahedron given Insphere Radius calculation can be explained with given input values -> 668.6516 = 9*sqrt(3)/2*((12*7)/(sqrt(3)*(3+sqrt(5))))^2.

### FAQ

What is Lateral Surface Area of Icosahedron given Insphere Radius?
The Lateral Surface Area of Icosahedron given Insphere Radius formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron and is calculated using the insphere radius of the Icosahedron and is represented as LSA = 9*sqrt(3)/2*((12*ri)/(sqrt(3)*(3+sqrt(5))))^2 or Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((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 Lateral Surface Area of Icosahedron given Insphere Radius?
The Lateral Surface Area of Icosahedron given Insphere Radius formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Icosahedron and is calculated using the insphere radius of the Icosahedron is calculated using Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2. To calculate Lateral Surface 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 Lateral Surface Area of Icosahedron?
In this formula, Lateral Surface Area of Icosahedron uses Insphere Radius of Icosahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
• Lateral Surface Area of Icosahedron = 9/10*Total Surface Area of Icosahedron
• Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Face Perimeter of Icosahedron/3)^2
• Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron
• Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*Edge Length of Icosahedron^2
• Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
• Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
• Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
• Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^2
• Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((12/5*Volume of Icosahedron)/(3+sqrt(5)))^(2/3)
• Lateral Surface Area of Icosahedron = Total Surface Area of Icosahedron-sqrt(3)/2*Edge Length of Icosahedron^2
• Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Perimeter of Icosahedron/30)^2 Let Others Know