Total Surface Area of Triakis Icosahedron given Midsphere Radius Calculator

✖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.ⓘ Midsphere Radius of Triakis Icosahedron [r_m]

+10%

-10%

✖The Total Surface Area of Triakis Icosahedron is the amount or quantity of two dimensional space covered on the surface of Triakis Icosahedron.ⓘ Total Surface Area of Triakis Icosahedron given Midsphere Radius [TSA]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download 3D Geometry Formula PDF PDF Image

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*r_m)/(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*r_m)/(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 00.007 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » CatalanSolids » Triakis Icosahedron » Total Surface Area of Triakis Icosahedron » Total Surface Area of Triakis Icosahedron given Midsphere Radius

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< Total Surface Area of Triakis Icosahedron Calculators

Total Surface Area of Triakis Icosahedron given Pyramidal Edge Length

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX Go

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 (r_m) 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*r_m)/(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 (r_m). 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 3 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))

Home

FREE PDFs

🔍 Search