Total Surface Area of Icosahedron given Lateral Surface Area Calculator

✖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.ⓘ Lateral Surface Area of Icosahedron [LSA]

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✖Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.ⓘ Total Surface Area of Icosahedron given Lateral Surface Area [TSA]

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Formula

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Total Surface Area of Icosahedron given Lateral Surface Area

Formula

`"TSA" = 10/9*"LSA"`

Example

`"866.6667m²"=10/9*"780m²"`

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Total Surface Area of Icosahedron given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Icosahedron = 10/9*Lateral Surface Area of Icosahedron
TSA = 10/9*LSA
This formula uses 2 Variables

Variables Used

Total Surface Area of Icosahedron - (Measured in Square Meter) - Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface 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

TSA = 10/9*LSA --> 10/9*780

Evaluating ... ...

TSA = 866.666666666667

STEP 3: Convert Result to Output's Unit

866.666666666667 Square Meter --> No Conversion Required

FINAL ANSWER

866.666666666667 ≈ 866.6667 Square Meter <-- Total Surface Area of Icosahedron

(Calculation completed in 00.020 seconds)

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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 Total Surface Area of Icosahedron Calculators

Total Surface Area of Icosahedron given Surface to Volume Ratio

Go Total Surface Area of Icosahedron = 5*sqrt(3)*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^2

Total Surface Area of Icosahedron given Circumsphere Radius

Go Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2

Total Surface Area of Icosahedron given Insphere Radius

Go Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2

Total Surface Area of Icosahedron given Space Diagonal

Go Total Surface Area of Icosahedron = 5*sqrt(3)*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2

Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length

Go Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2

Total Surface Area of Icosahedron given Midsphere Radius

Go Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2

Total Surface Area of Icosahedron given Volume

Go Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(2/3)

Total Surface Area of Icosahedron given Face Perimeter

Go Total Surface Area of Icosahedron = 5*sqrt(3)*(Face Perimeter of Icosahedron/3)^2

Total Surface Area of Icosahedron given Perimeter

Go Total Surface Area of Icosahedron = 5*sqrt(3)*(Perimeter of Icosahedron/30)^2

Total Surface Area of Icosahedron

Go Total Surface Area of Icosahedron = 5*sqrt(3)*Edge Length of Icosahedron^2

Total Surface Area of Icosahedron given Lateral Surface Area

Go Total Surface Area of Icosahedron = 10/9*Lateral Surface Area of Icosahedron

Total Surface Area of Icosahedron given Face Area

Go Total Surface Area of Icosahedron = 20*Face Area of Icosahedron

Total Surface Area of Icosahedron given Lateral Surface Area Formula

Total Surface Area of Icosahedron = 10/9*Lateral Surface Area of Icosahedron
TSA = 10/9*LSA

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 Total Surface Area of Icosahedron given Lateral Surface Area?

Total Surface Area of Icosahedron given Lateral Surface Area calculator uses Total Surface Area of Icosahedron = 10/9*Lateral Surface Area of Icosahedron to calculate the Total Surface Area of Icosahedron, The Total Surface Area of Icosahedron given Lateral Surface Area formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron, and calculated using the lateral surface area of the Icosahedron. Total Surface Area of Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Icosahedron given Lateral Surface Area using this online calculator? To use this online calculator for Total Surface Area of Icosahedron given Lateral Surface Area, enter Lateral Surface Area of Icosahedron (LSA) and hit the calculate button. Here is how the Total Surface Area of Icosahedron given Lateral Surface Area calculation can be explained with given input values -> 866.6667 = 10/9*780.

FAQ

What is Total Surface Area of Icosahedron given Lateral Surface Area?

The Total Surface Area of Icosahedron given Lateral Surface Area formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron, and calculated using the lateral surface area of the Icosahedron and is represented as TSA = 10/9*LSA or Total Surface Area of Icosahedron = 10/9*Lateral Surface Area of Icosahedron. 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 Total Surface Area of Icosahedron given Lateral Surface Area?

The Total Surface Area of Icosahedron given Lateral Surface Area formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron, and calculated using the lateral surface area of the Icosahedron is calculated using Total Surface Area of Icosahedron = 10/9*Lateral Surface Area of Icosahedron. To calculate Total Surface Area 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 Total Surface Area of Icosahedron?

In this formula, Total Surface Area of Icosahedron uses Lateral Surface Area of Icosahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(2/3)
Total Surface Area of Icosahedron = 5*sqrt(3)*Edge Length of Icosahedron^2
Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Total Surface Area of Icosahedron = 5*sqrt(3)*(Face Perimeter of Icosahedron/3)^2
Total Surface Area of Icosahedron = 20*Face Area of Icosahedron
Total Surface Area of Icosahedron = Lateral Surface Area of Icosahedron+sqrt(3)/2*Edge Length of Icosahedron^2
Total Surface Area of Icosahedron = 5*sqrt(3)*(Perimeter of Icosahedron/30)^2

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