Total Surface Area of Triakis Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))^2)
TSA = (15/11)*(sqrt(109-(30*sqrt(5))))*(((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
Total Surface Area of Triakis Icosahedron - (Measured in Square Meter) - The Total Surface Area of Triakis Icosahedron is the amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron.
Midsphere Radius of Triakis Icosahedron - (Measured in Meter) - Midsphere Radius of Triakis Icosahedron is the radius of the sphere for which all the edges of the Triakis Icosahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Triakis Icosahedron: 7 Meter --> 7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*rm)/(1+sqrt(5)))^2) --> (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*7)/(1+sqrt(5)))^2)
Evaluating ... ...
TSA = 660.966483501772
STEP 3: Convert Result to Output's Unit
660.966483501772 Square Meter --> No Conversion Required
FINAL ANSWER
660.966483501772 660.9665 Square Meter <-- Total Surface Area of Triakis Icosahedron
(Calculation completed in 00.004 seconds)

Credits

Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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Indian Institute of Information Technology (IIIT), Bhopal
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6 Total Surface Area of Triakis Icosahedron Calculators

Total Surface Area of Triakis Icosahedron given Surface to Volume Ratio
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Surface to Volume Ratio of Triakis Icosahedron))^2)
Total Surface Area of Triakis Icosahedron given Insphere Radius
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2)
Total Surface Area of Triakis Icosahedron given Pyramidal Edge Length
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))^2)
Total Surface Area of Triakis Icosahedron given Volume
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((44*Volume of Triakis Icosahedron)/(5*(5+(7*sqrt(5)))))^(2/3))
Total Surface Area of Triakis Icosahedron given Midsphere Radius
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))^2)
Total Surface Area of Triakis Icosahedron
Go Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*((Icosahedral Edge Length of Triakis Icosahedron)^2)

Total Surface Area of Triakis Icosahedron given Midsphere Radius Formula

Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))^2)
TSA = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*rm)/(1+sqrt(5)))^2)

What is Triakis Icosahedron?

The Triakis Icosahedron is a three-dimensional polyhedron created from the dual of the truncated dodecahedron. Because of this, it shares the same full icosahedral symmetry group as the dodecahedron and the truncated dodecahedron. It can also be constructed by adding short triangular pyramids onto the faces of an icosahedron. It has 60 faces, 90 edges, 32 vertices.

How to Calculate Total Surface Area of Triakis Icosahedron given Midsphere Radius?

Total Surface Area of Triakis Icosahedron given Midsphere Radius calculator uses Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))^2) to calculate the Total Surface Area of Triakis Icosahedron, Total Surface Area of Triakis Icosahedron given Midsphere Radius formula is defined as the amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron, calculated using midsphere radius of Triakis Icosahedron. Total Surface Area of Triakis Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Triakis Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Triakis Icosahedron given Midsphere Radius, enter Midsphere Radius of Triakis Icosahedron (rm) and hit the calculate button. Here is how the Total Surface Area of Triakis Icosahedron given Midsphere Radius calculation can be explained with given input values -> 660.9665 = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*7)/(1+sqrt(5)))^2).

FAQ

What is Total Surface Area of Triakis Icosahedron given Midsphere Radius?
Total Surface Area of Triakis Icosahedron given Midsphere Radius formula is defined as the amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron, calculated using midsphere radius of Triakis Icosahedron and is represented as TSA = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*rm)/(1+sqrt(5)))^2) or Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))^2). Midsphere Radius of Triakis Icosahedron is the radius of the sphere for which all the edges of the Triakis Icosahedron become a tangent line on that sphere.
How to calculate Total Surface Area of Triakis Icosahedron given Midsphere Radius?
Total Surface Area of Triakis Icosahedron given Midsphere Radius formula is defined as the amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron, calculated using midsphere radius of Triakis Icosahedron is calculated using Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))^2). To calculate Total Surface Area of Triakis Icosahedron given Midsphere Radius, you need Midsphere Radius of Triakis Icosahedron (rm). With our tool, you need to enter the respective value for Midsphere Radius of Triakis 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 Triakis Icosahedron?
In this formula, Total Surface Area of Triakis Icosahedron uses Midsphere Radius of Triakis Icosahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*((Icosahedral Edge Length of Triakis Icosahedron)^2)
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))^2)
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((44*Volume of Triakis Icosahedron)/(5*(5+(7*sqrt(5)))))^(2/3))
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^2)
  • Total Surface Area of Triakis Icosahedron = (15/11)*(sqrt(109-(30*sqrt(5))))*(((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Surface to Volume Ratio of Triakis Icosahedron))^2)
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