Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius Calculator

✖Insphere Radius of Pentagonal Icositetrahedron is the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere.ⓘ Insphere Radius of Pentagonal Icositetrahedron [r_i]

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✖Total Surface Area of Pentagonal Icositetrahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Icositetrahedron.ⓘ Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius [TSA]

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Formula

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Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius

Formula

`"TSA" = 3*(2*sqrt((2-"[Tribonacci_C]")*(3-"[Tribonacci_C]"))*"r"_{"i"})^2*sqrt((22*(5*"[Tribonacci_C]"-1))/((4*"[Tribonacci_C]")-3))`

Example

`"2073.686m²"=3*(2*sqrt((2-"[Tribonacci_C]")*(3-"[Tribonacci_C]"))*"12m")^2*sqrt((22*(5*"[Tribonacci_C]"-1))/((4*"[Tribonacci_C]")-3))`

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Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Pentagonal Icositetrahedron = 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*Insphere Radius of Pentagonal Icositetrahedron)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))
TSA = 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*r_i)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[Tribonacci_C] - Tribonacci constant Value Taken As 1.839286755214161

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 Pentagonal Icositetrahedron - (Measured in Square Meter) - Total Surface Area of Pentagonal Icositetrahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Icositetrahedron.
Insphere Radius of Pentagonal Icositetrahedron - (Measured in Meter) - Insphere Radius of Pentagonal Icositetrahedron is the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Pentagonal Icositetrahedron: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*r_i)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)) --> 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*12)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))

Evaluating ... ...

TSA = 2073.68625113801

STEP 3: Convert Result to Output's Unit

2073.68625113801 Square Meter --> No Conversion Required

FINAL ANSWER

2073.68625113801 ≈ 2073.686 Square Meter <-- Total Surface Area of Pentagonal Icositetrahedron

(Calculation completed in 00.020 seconds)

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< 7 Surface Area of Pentagonal Icositetrahedron Calculators

Total Surface Area of Pentagonal Icositetrahedron given Surface to Volume Ratio

Go Total Surface Area of Pentagonal Icositetrahedron = 3*((3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(SA:V of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))))^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))

Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius

Go Total Surface Area of Pentagonal Icositetrahedron = 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*Insphere Radius of Pentagonal Icositetrahedron)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))

Total Surface Area of Pentagonal Icositetrahedron given Volume

Go Total Surface Area of Pentagonal Icositetrahedron = 3*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))

Total Surface Area of Pentagonal Icositetrahedron given Midsphere Radius

Go Total Surface Area of Pentagonal Icositetrahedron = 3*(2*sqrt(2-[Tribonacci_C])*Midsphere Radius of Pentagonal Icositetrahedron)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))

Total Surface Area of Pentagonal Icositetrahedron given Long Edge

Go Total Surface Area of Pentagonal Icositetrahedron = 3*((2*Long Edge of Pentagonal Icositetrahedron)/sqrt([Tribonacci_C]+1))^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))

Total Surface Area of Pentagonal Icositetrahedron given Short Edge

Go Total Surface Area of Pentagonal Icositetrahedron = 3*(sqrt([Tribonacci_C]+1)*Short Edge of Pentagonal Icositetrahedron)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))

Total Surface Area of Pentagonal Icositetrahedron

Go Total Surface Area of Pentagonal Icositetrahedron = 3*Snub Cube Edge of Pentagonal Icositetrahedron^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))

Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius Formula

What is Pentagonal Icositetrahedron?

The Pentagonal Icositetrahedron can be constructed from a snub cube. Its faces are axial-symmetric pentagons with the top angle acos(2-t)=80.7517°. Of this polyhedron, there are two forms that are mirror images of each other, but otherwise identical. It has 24 faces, 60 edges, and 38 vertices.

How to Calculate Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius?

Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius calculator uses Total Surface Area of Pentagonal Icositetrahedron = 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*Insphere Radius of Pentagonal Icositetrahedron)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)) to calculate the Total Surface Area of Pentagonal Icositetrahedron, Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius formula is defined as the amount or quantity of two dimensional space covered on the surface of Pentagonal Icositetrahedron, calculated using insphere radius of Pentagonal Icositetrahedron. Total Surface Area of Pentagonal Icositetrahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius using this online calculator? To use this online calculator for Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius, enter Insphere Radius of Pentagonal Icositetrahedron (r_i) and hit the calculate button. Here is how the Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius calculation can be explained with given input values -> 2073.686 = 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*12)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)).

FAQ

What is Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius?

Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius formula is defined as the amount or quantity of two dimensional space covered on the surface of Pentagonal Icositetrahedron, calculated using insphere radius of Pentagonal Icositetrahedron and is represented as TSA = 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*r_i)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)) or Total Surface Area of Pentagonal Icositetrahedron = 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*Insphere Radius of Pentagonal Icositetrahedron)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)). Insphere Radius of Pentagonal Icositetrahedron is the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere.

How to calculate Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius?

Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius formula is defined as the amount or quantity of two dimensional space covered on the surface of Pentagonal Icositetrahedron, calculated using insphere radius of Pentagonal Icositetrahedron is calculated using Total Surface Area of Pentagonal Icositetrahedron = 3*(2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*Insphere Radius of Pentagonal Icositetrahedron)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)). To calculate Total Surface Area of Pentagonal Icositetrahedron given Insphere Radius, you need Insphere Radius of Pentagonal Icositetrahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Pentagonal Icositetrahedron 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 Pentagonal Icositetrahedron?

In this formula, Total Surface Area of Pentagonal Icositetrahedron uses Insphere Radius of Pentagonal Icositetrahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Pentagonal Icositetrahedron = 3*Snub Cube Edge of Pentagonal Icositetrahedron^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))
Total Surface Area of Pentagonal Icositetrahedron = 3*(sqrt([Tribonacci_C]+1)*Short Edge of Pentagonal Icositetrahedron)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))
Total Surface Area of Pentagonal Icositetrahedron = 3*((2*Long Edge of Pentagonal Icositetrahedron)/sqrt([Tribonacci_C]+1))^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))
Total Surface Area of Pentagonal Icositetrahedron = 3*(Volume of Pentagonal Icositetrahedron^(1/3)*((2*((20*[Tribonacci_C])-37))/(11*([Tribonacci_C]-4)))^(1/6))^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))
Total Surface Area of Pentagonal Icositetrahedron = 3*((3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(SA:V of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))))^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))
Total Surface Area of Pentagonal Icositetrahedron = 3*(2*sqrt(2-[Tribonacci_C])*Midsphere Radius of Pentagonal Icositetrahedron)^2*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3))

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