Total Surface Area of Icosahedron given Face Perimeter Calculator

✖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 Face Perimeter [TSA]

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Total Surface Area of Icosahedron given Face Perimeter

Formula

`"TSA" = 5*sqrt(3)*("P"_{"Face"}/3)^2`

Example

`"866.0254m²"=5*sqrt(3)*("30m"/3)^2`

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Total Surface Area of Icosahedron given Face Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Face Perimeter of Icosahedron - (Measured in Meter) - Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Face Perimeter of Icosahedron: 30 Meter --> 30 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 5*sqrt(3)*(P_Face/3)^2 --> 5*sqrt(3)*(30/3)^2

Evaluating ... ...

TSA = 866.025403784439

STEP 3: Convert Result to Output's Unit

866.025403784439 Square Meter --> No Conversion Required

FINAL ANSWER

866.025403784439 ≈ 866.0254 Square Meter <-- Total Surface Area of Icosahedron

(Calculation completed in 00.004 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 Face Perimeter Formula

Total Surface Area of Icosahedron = 5*sqrt(3)*(Face Perimeter of Icosahedron/3)^2
TSA = 5*sqrt(3)*(P_Face/3)^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 Total Surface Area of Icosahedron given Face Perimeter?

Total Surface Area of Icosahedron given Face Perimeter calculator uses Total Surface Area of Icosahedron = 5*sqrt(3)*(Face Perimeter of Icosahedron/3)^2 to calculate the Total Surface Area of Icosahedron, The Total Surface Area of Icosahedron given Face Perimeter formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron, and calculated using the face perimeter of the Icosahedron. Total Surface Area of Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Icosahedron given Face Perimeter using this online calculator? To use this online calculator for Total Surface Area of Icosahedron given Face Perimeter, enter Face Perimeter of Icosahedron (P_Face) and hit the calculate button. Here is how the Total Surface Area of Icosahedron given Face Perimeter calculation can be explained with given input values -> 866.0254 = 5*sqrt(3)*(30/3)^2.

FAQ

What is Total Surface Area of Icosahedron given Face Perimeter?

The Total Surface Area of Icosahedron given Face Perimeter formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron, and calculated using the face perimeter of the Icosahedron and is represented as TSA = 5*sqrt(3)*(P_Face/3)^2 or Total Surface Area of Icosahedron = 5*sqrt(3)*(Face Perimeter of Icosahedron/3)^2. Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.

How to calculate Total Surface Area of Icosahedron given Face Perimeter?

The Total Surface Area of Icosahedron given Face Perimeter formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron, and calculated using the face perimeter of the Icosahedron is calculated using Total Surface Area of Icosahedron = 5*sqrt(3)*(Face Perimeter of Icosahedron/3)^2. To calculate Total Surface Area of Icosahedron given Face Perimeter, you need Face Perimeter of Icosahedron (P_Face). With our tool, you need to enter the respective value for Face Perimeter 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 Face Perimeter 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 = 20*Face Area of Icosahedron
Total Surface Area of Icosahedron = 10/9*Lateral Surface 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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