## Lateral Surface Area of Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
LSA = 9*sqrt(3)/2*((4*rm)/(1+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
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.
Midsphere Radius of Icosahedron - (Measured in Meter) - The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Icosahedron: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
LSA = 9*sqrt(3)/2*((4*rm)/(1+sqrt(5)))^2 --> 9*sqrt(3)/2*((4*8)/(1+sqrt(5)))^2
Evaluating ... ...
LSA = 762.145388063548
STEP 3: Convert Result to Output's Unit
762.145388063548 Square Meter --> No Conversion Required
762.145388063548 762.1454 Square Meter <-- Lateral Surface Area of Icosahedron
(Calculation completed in 00.020 seconds)
You are here -
Home » Math »

## Credits

Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
Dhruv Walia has created this Calculator and 1100+ more calculators!
Verified by Nikhil
Mumbai University (DJSCE), Mumbai
Nikhil has verified this Calculator and 300+ more calculators!

## < 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 Midsphere Radius Formula

Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
LSA = 9*sqrt(3)/2*((4*rm)/(1+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 Midsphere Radius?

Lateral Surface Area of Icosahedron given Midsphere Radius calculator uses Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2 to calculate the Lateral Surface Area of Icosahedron, The Lateral Surface Area of Icosahedron given Midsphere 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 midsphere radius of the Icosahedron. Lateral Surface Area of Icosahedron is denoted by LSA symbol.

How to calculate Lateral Surface Area of Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Lateral Surface Area of Icosahedron given Midsphere Radius, enter Midsphere Radius of Icosahedron (rm) and hit the calculate button. Here is how the Lateral Surface Area of Icosahedron given Midsphere Radius calculation can be explained with given input values -> 762.1454 = 9*sqrt(3)/2*((4*8)/(1+sqrt(5)))^2.

### FAQ

What is Lateral Surface Area of Icosahedron given Midsphere Radius?
The Lateral Surface Area of Icosahedron given Midsphere 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 midsphere radius of the Icosahedron and is represented as LSA = 9*sqrt(3)/2*((4*rm)/(1+sqrt(5)))^2 or Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2. The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.
How to calculate Lateral Surface Area of Icosahedron given Midsphere Radius?
The Lateral Surface Area of Icosahedron given Midsphere 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 midsphere radius of the Icosahedron is calculated using Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2. To calculate Lateral Surface Area of Icosahedron given Midsphere Radius, you need Midsphere Radius of Icosahedron (rm). With our tool, you need to enter the respective value for Midsphere 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 Midsphere 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*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+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