Total Surface Area of Great Icosahedron given Long Ridge Length Calculator

✖Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.ⓘ Long Ridge Length of Great Icosahedron [l_Ridge(Long)]

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✖Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.ⓘ Total Surface Area of Great Icosahedron given Long Ridge Length [TSA]

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Formula

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Total Surface Area of Great Icosahedron given Long Ridge Length

Formula

`"TSA" = 3*sqrt(3)*(5+4*sqrt(5))*((10*"l"_{"Ridge(Long)"})/(sqrt(2)*(5+(3*sqrt(5)))))^2`

Example

`"7637.743m²"=3*sqrt(3)*(5+4*sqrt(5))*((10*"17m")/(sqrt(2)*(5+(3*sqrt(5)))))^2`

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Total Surface Area of Great Icosahedron given Long Ridge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^2
TSA = 3*sqrt(3)*(5+4*sqrt(5))*((10*l_Ridge(Long))/(sqrt(2)*(5+(3*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 Great Icosahedron - (Measured in Square Meter) - Total Surface Area of Great Icosahedron is the total quantity of plane enclosed on the entire surface of the Great Icosahedron.
Long Ridge Length of Great Icosahedron - (Measured in Meter) - Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.

STEP 1: Convert Input(s) to Base Unit

Long Ridge Length of Great Icosahedron: 17 Meter --> 17 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 3*sqrt(3)*(5+4*sqrt(5))*((10*l_Ridge(Long))/(sqrt(2)*(5+(3*sqrt(5)))))^2 --> 3*sqrt(3)*(5+4*sqrt(5))*((10*17)/(sqrt(2)*(5+(3*sqrt(5)))))^2

Evaluating ... ...

TSA = 7637.74255131048

STEP 3: Convert Result to Output's Unit

7637.74255131048 Square Meter --> No Conversion Required

FINAL ANSWER

7637.74255131048 ≈ 7637.743 Square Meter <-- Total Surface Area of Great Icosahedron

(Calculation completed in 00.004 seconds)

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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

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< 7 Total Surface Area of Great Icosahedron Calculators

Total Surface Area of Great Icosahedron given Surface to Volume Ratio

Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^2

Total Surface Area of Great Icosahedron given Long Ridge Length

Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^2

Total Surface Area of Great Icosahedron given Circumsphere Radius

Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5)))))^2

Total Surface Area of Great Icosahedron given Mid Ridge Length

Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)))^2

Total Surface Area of Great Icosahedron given Short Ridge Length

Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((5*Short Ridge Length of Great Icosahedron)/sqrt(10))^2

Total Surface Area of Great Icosahedron given Volume

Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(2/3)

Total Surface Area of Great Icosahedron

Go Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*Edge Length of Great Icosahedron^2

Total Surface Area of Great Icosahedron given Long Ridge Length Formula

What is Great Icosahedron?

The Great Icosahedron can be constructed from an icosahedron with unit edge lengths by taking the 20 sets of vertices that are mutually spaced by a distance phi, the golden ratio. The solid therefore consists of 20 equilateral triangles. The symmetry of their arrangement is such that the resulting solid contains 12 pentagrams.

How to Calculate Total Surface Area of Great Icosahedron given Long Ridge Length?

Total Surface Area of Great Icosahedron given Long Ridge Length calculator uses Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^2 to calculate the Total Surface Area of Great Icosahedron, Total Surface Area of Great Icosahedron given Long Ridge Length formula is defined as the total quantity of plane enclosed by the entire surface of the Great Icosahedron, calculated using long ridge length. Total Surface Area of Great Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Icosahedron given Long Ridge Length using this online calculator? To use this online calculator for Total Surface Area of Great Icosahedron given Long Ridge Length, enter Long Ridge Length of Great Icosahedron (l_Ridge(Long)) and hit the calculate button. Here is how the Total Surface Area of Great Icosahedron given Long Ridge Length calculation can be explained with given input values -> 7637.743 = 3*sqrt(3)*(5+4*sqrt(5))*((10*17)/(sqrt(2)*(5+(3*sqrt(5)))))^2.

FAQ

What is Total Surface Area of Great Icosahedron given Long Ridge Length?

Total Surface Area of Great Icosahedron given Long Ridge Length formula is defined as the total quantity of plane enclosed by the entire surface of the Great Icosahedron, calculated using long ridge length and is represented as TSA = 3*sqrt(3)*(5+4*sqrt(5))*((10*l_Ridge(Long))/(sqrt(2)*(5+(3*sqrt(5)))))^2 or Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^2. Long Ridge Length of Great Icosahedron is the length of any of the edges that connects the peak vertex and adjacent vertex of the pentagon on which each peak of Great Icosahedron is attached.

How to calculate Total Surface Area of Great Icosahedron given Long Ridge Length?

Total Surface Area of Great Icosahedron given Long Ridge Length formula is defined as the total quantity of plane enclosed by the entire surface of the Great Icosahedron, calculated using long ridge length is calculated using Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((10*Long Ridge Length of Great Icosahedron)/(sqrt(2)*(5+(3*sqrt(5)))))^2. To calculate Total Surface Area of Great Icosahedron given Long Ridge Length, you need Long Ridge Length of Great Icosahedron (l_Ridge(Long)). With our tool, you need to enter the respective value for Long Ridge Length of Great 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 Great Icosahedron?

In this formula, Total Surface Area of Great Icosahedron uses Long Ridge Length of Great Icosahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*Edge Length of Great Icosahedron^2
Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((2*Mid Ridge Length of Great Icosahedron)/(1+sqrt(5)))^2
Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((5*Short Ridge Length of Great Icosahedron)/sqrt(10))^2
Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((4*Circumsphere Radius of Great Icosahedron)/(sqrt(50+(22*sqrt(5)))))^2
Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((4*Volume of Great Icosahedron)/(25+(9*sqrt(5))))^(2/3)
Total Surface Area of Great Icosahedron = 3*sqrt(3)*(5+4*sqrt(5))*((3*sqrt(3)*(5+(4*sqrt(5))))/(1/4*(25+(9*sqrt(5)))*Surface to Volume Ratio of Great Icosahedron))^2

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