Total Surface Area of Pentagonal Hexecontahedron given Long Edge Calculator

✖Long Edge of Pentagonal Hexecontahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron.ⓘ Long Edge of Pentagonal Hexecontahedron [l_e(Long)]

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✖Total Surface Area of Pentagonal Hexecontahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Hexecontahedron.ⓘ Total Surface Area of Pentagonal Hexecontahedron given Long Edge [TSA]

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Total Surface Area of Pentagonal Hexecontahedron given Long Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Pentagonal Hexecontahedron = 30*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
TSA = 30*((31*l_e(Long))/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811

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 Hexecontahedron - (Measured in Square Meter) - Total Surface Area of Pentagonal Hexecontahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Hexecontahedron.
Long Edge of Pentagonal Hexecontahedron - (Measured in Meter) - Long Edge of Pentagonal Hexecontahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron.

STEP 1: Convert Input(s) to Base Unit

Long Edge of Pentagonal Hexecontahedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 30*((31*l_e(Long))/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2) --> 30*((31*6)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)

Evaluating ... ...

TSA = 3132.67759508438

STEP 3: Convert Result to Output's Unit

3132.67759508438 Square Meter --> No Conversion Required

FINAL ANSWER

3132.67759508438 ≈ 3132.678 Square Meter <-- Total Surface Area of Pentagonal Hexecontahedron

(Calculation completed in 00.004 seconds)

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< Surface Area of Pentagonal Hexecontahedron Calculators

Total Surface Area of Pentagonal Hexecontahedron given Long Edge

LaTeX Go Total Surface Area of Pentagonal Hexecontahedron = 30*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)

Total Surface Area of Pentagonal Hexecontahedron given Volume

LaTeX Go Total Surface Area of Pentagonal Hexecontahedron = 30*((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)))^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)

Total Surface Area of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

LaTeX Go Total Surface Area of Pentagonal Hexecontahedron = 30*(Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)

Total Surface Area of Pentagonal Hexecontahedron

LaTeX Go Total Surface Area of Pentagonal Hexecontahedron = 30*Short Edge of Pentagonal Hexecontahedron^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)

Total Surface Area of Pentagonal Hexecontahedron given Long Edge Formula

LaTeX Go

What is Pentagonal Hexecontahedron?

In geometry, a Pentagonal Hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. It has 60 faces, 150 edges, 92 vertices. It is the Catalan solid with the most vertices. Among the Catalan and Archimedean solids, it has the second largest number of vertices, after the truncated icosidodecahedron, which has 120 vertices.

How to Calculate Total Surface Area of Pentagonal Hexecontahedron given Long Edge?

Total Surface Area of Pentagonal Hexecontahedron given Long Edge calculator uses Total Surface Area of Pentagonal Hexecontahedron = 30*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2) to calculate the Total Surface Area of Pentagonal Hexecontahedron, Total Surface Area of Pentagonal Hexecontahedron given Long Edge formula is defined as the amount or quantity of two-dimensional space covered by the surface of the Pentagonal Hexecontahedron, calculated using long edge of Pentagonal Hexecontahedron. Total Surface Area of Pentagonal Hexecontahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Pentagonal Hexecontahedron given Long Edge using this online calculator? To use this online calculator for Total Surface Area of Pentagonal Hexecontahedron given Long Edge, enter Long Edge of Pentagonal Hexecontahedron (l_e(Long)) and hit the calculate button. Here is how the Total Surface Area of Pentagonal Hexecontahedron given Long Edge calculation can be explained with given input values -> 3132.678 = 30*((31*6)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2).

FAQ

What is Total Surface Area of Pentagonal Hexecontahedron given Long Edge?

Total Surface Area of Pentagonal Hexecontahedron given Long Edge formula is defined as the amount or quantity of two-dimensional space covered by the surface of the Pentagonal Hexecontahedron, calculated using long edge of Pentagonal Hexecontahedron and is represented as TSA = 30*((31*l_e(Long))/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2) or Total Surface Area of Pentagonal Hexecontahedron = 30*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2). Long Edge of Pentagonal Hexecontahedron is the length of longest edge which is the top edge of the axial-symmetric pentagonal faces of Pentagonal Hexecontahedron.

How to calculate Total Surface Area of Pentagonal Hexecontahedron given Long Edge?

Total Surface Area of Pentagonal Hexecontahedron given Long Edge formula is defined as the amount or quantity of two-dimensional space covered by the surface of the Pentagonal Hexecontahedron, calculated using long edge of Pentagonal Hexecontahedron is calculated using Total Surface Area of Pentagonal Hexecontahedron = 30*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2). To calculate Total Surface Area of Pentagonal Hexecontahedron given Long Edge, you need Long Edge of Pentagonal Hexecontahedron (l_e(Long)). With our tool, you need to enter the respective value for Long Edge of Pentagonal Hexecontahedron 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 Hexecontahedron?

In this formula, Total Surface Area of Pentagonal Hexecontahedron uses Long Edge of Pentagonal Hexecontahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Pentagonal Hexecontahedron = 30*Short Edge of Pentagonal Hexecontahedron^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
Total Surface Area of Pentagonal Hexecontahedron = 30*(Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
Total Surface Area of Pentagonal Hexecontahedron = 30*((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)))^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)

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