Lateral Surface Area of Icosahedron given Face Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron
LSA = 18*AFace
This formula uses 2 Variables
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.
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.
STEP 1: Convert Input(s) to Base Unit
Face Area of Icosahedron: 45 Square Meter --> 45 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
LSA = 18*AFace --> 18*45
Evaluating ... ...
LSA = 810
STEP 3: Convert Result to Output's Unit
810 Square Meter --> No Conversion Required
FINAL ANSWER
810 Square Meter <-- Lateral Surface 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 Lateral Surface Area of Icosahedron Calculators

Lateral Surface Area of Icosahedron given Surface to Volume Ratio
​ Go 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
​ Go 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
​ Go 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
​ Go 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
​ Go 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
​ Go 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
​ Go 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
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Face Perimeter of Icosahedron/3)^2
Lateral Surface Area of Icosahedron given Perimeter
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*(Perimeter of Icosahedron/30)^2
Lateral Surface Area of Icosahedron
​ Go Lateral Surface Area of Icosahedron = 9*sqrt(3)/2*Edge Length of Icosahedron^2
Lateral Surface Area of Icosahedron given Total Surface Area
​ Go Lateral Surface Area of Icosahedron = 9/10*Total Surface Area of Icosahedron
Lateral Surface Area of Icosahedron given Face Area
​ Go Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron

Lateral Surface Area of Icosahedron given Face Area Formula

Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron
LSA = 18*AFace

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 Face Area?

Lateral Surface Area of Icosahedron given Face Area calculator uses Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron to calculate the Lateral Surface Area of Icosahedron, The Lateral Surface Area of Icosahedron given Face Area 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 face area of the Icosahedron. Lateral Surface Area of Icosahedron is denoted by LSA symbol.

How to calculate Lateral Surface Area of Icosahedron given Face Area using this online calculator? To use this online calculator for Lateral Surface Area of Icosahedron given Face Area, enter Face Area of Icosahedron (AFace) and hit the calculate button. Here is how the Lateral Surface Area of Icosahedron given Face Area calculation can be explained with given input values -> 810 = 18*45.

FAQ

What is Lateral Surface Area of Icosahedron given Face Area?
The Lateral Surface Area of Icosahedron given Face Area 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 face area of the Icosahedron and is represented as LSA = 18*AFace or Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron. The Face Area of Icosahedron is the amount of space occupied by any one of the 12 faces of Icosahedron.
How to calculate Lateral Surface Area of Icosahedron given Face Area?
The Lateral Surface Area of Icosahedron given Face Area 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 face area of the Icosahedron is calculated using Lateral Surface Area of Icosahedron = 18*Face Area of Icosahedron. To calculate Lateral Surface Area of Icosahedron given Face Area, you need Face Area of Icosahedron (AFace). With our tool, you need to enter the respective value for Face Area 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 Face Area 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 = 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*((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
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