Perimeter of Icosahedron given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Perimeter of Icosahedron = 30*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
P = 30*sqrt((2*LSA)/(9*sqrt(3)))
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
Perimeter of Icosahedron - (Measured in Meter) - Perimeter of Icosahedron is the sum of the total distance around all the edges of the Icosahedron.
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.
STEP 1: Convert Input(s) to Base Unit
Lateral Surface Area of Icosahedron: 780 Square Meter --> 780 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = 30*sqrt((2*LSA)/(9*sqrt(3))) --> 30*sqrt((2*780)/(9*sqrt(3)))
Evaluating ... ...
P = 300.111049436007
STEP 3: Convert Result to Output's Unit
300.111049436007 Meter --> No Conversion Required
FINAL ANSWER
300.111049436007 300.111 Meter <-- Perimeter 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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Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI
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11 Perimeter of Icosahedron Calculators

Perimeter of Icosahedron given Surface to Volume Ratio
​ Go Perimeter of Icosahedron = (360*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Perimeter of Icosahedron given Circumsphere Radius
​ Go Perimeter of Icosahedron = (120*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Perimeter of Icosahedron given Lateral Surface Area
​ Go Perimeter of Icosahedron = 30*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Perimeter of Icosahedron given Insphere Radius
​ Go Perimeter of Icosahedron = (360*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Perimeter of Icosahedron given Space Diagonal
​ Go Perimeter of Icosahedron = (60*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))
Perimeter of Icosahedron given Total Surface Area
​ Go Perimeter of Icosahedron = 30*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Perimeter of Icosahedron given Face Area
​ Go Perimeter of Icosahedron = 30*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Perimeter of Icosahedron given Volume
​ Go Face Perimeter of Icosahedron = 30*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
Perimeter of Icosahedron given Midsphere Radius
​ Go Perimeter of Icosahedron = (120*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Perimeter of Icosahedron given Face Perimeter
​ Go Perimeter of Icosahedron = 10*Face Perimeter of Icosahedron
Perimeter of Icosahedron
​ Go Perimeter of Icosahedron = 30*Edge Length of Icosahedron

Perimeter of Icosahedron given Lateral Surface Area Formula

Perimeter of Icosahedron = 30*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
P = 30*sqrt((2*LSA)/(9*sqrt(3)))

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 Perimeter of Icosahedron given Lateral Surface Area?

Perimeter of Icosahedron given Lateral Surface Area calculator uses Perimeter of Icosahedron = 30*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))) to calculate the Perimeter of Icosahedron, The Perimeter of Icosahedron given Lateral Surface Area formula is defined as the sum of the total distance around all the edges of the Icosahedron and is calculated using the lateral surface area of the Icosahedron. Perimeter of Icosahedron is denoted by P symbol.

How to calculate Perimeter of Icosahedron given Lateral Surface Area using this online calculator? To use this online calculator for Perimeter of Icosahedron given Lateral Surface Area, enter Lateral Surface Area of Icosahedron (LSA) and hit the calculate button. Here is how the Perimeter of Icosahedron given Lateral Surface Area calculation can be explained with given input values -> 300.111 = 30*sqrt((2*780)/(9*sqrt(3))).

FAQ

What is Perimeter of Icosahedron given Lateral Surface Area?
The Perimeter of Icosahedron given Lateral Surface Area formula is defined as the sum of the total distance around all the edges of the Icosahedron and is calculated using the lateral surface area of the Icosahedron and is represented as P = 30*sqrt((2*LSA)/(9*sqrt(3))) or Perimeter of Icosahedron = 30*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))). 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.
How to calculate Perimeter of Icosahedron given Lateral Surface Area?
The Perimeter of Icosahedron given Lateral Surface Area formula is defined as the sum of the total distance around all the edges of the Icosahedron and is calculated using the lateral surface area of the Icosahedron is calculated using Perimeter of Icosahedron = 30*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))). To calculate Perimeter of Icosahedron given Lateral Surface Area, you need Lateral Surface Area of Icosahedron (LSA). With our tool, you need to enter the respective value for Lateral Surface 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 Perimeter of Icosahedron?
In this formula, Perimeter of Icosahedron uses Lateral Surface Area of Icosahedron. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • Perimeter of Icosahedron = 30*Edge Length of Icosahedron
  • Perimeter of Icosahedron = (120*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))
  • Perimeter of Icosahedron = 30*sqrt((4*Face Area of Icosahedron)/sqrt(3))
  • Perimeter of Icosahedron = (360*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
  • Perimeter of Icosahedron = (120*Midsphere Radius of Icosahedron)/(1+sqrt(5))
  • Perimeter of Icosahedron = 10*Face Perimeter of Icosahedron
  • Perimeter of Icosahedron = (60*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))
  • Perimeter of Icosahedron = (360*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
  • Perimeter of Icosahedron = 30*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
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