Total Surface Area of Great Dodecahedron Calculator

✖Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.ⓘ Edge Length of Great Dodecahedron [l_e]

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✖Total Surface Area of Great Dodecahedron is the total quantity of plane enclosed on the entire surface of the Great Dodecahedron.ⓘ Total Surface Area of Great Dodecahedron [TSA]

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Formula

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Total Surface Area of Great Dodecahedron

Formula

`"TSA" = 15*sqrt(5-(2*sqrt(5)))*"l"_{"e"}^2`

Example

`"1089.814m²"=15*sqrt(5-(2*sqrt(5)))*("10m")^2`

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Total Surface Area of Great Dodecahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*Edge Length of Great Dodecahedron^2
TSA = 15*sqrt(5-(2*sqrt(5)))*l_e^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 Dodecahedron - (Measured in Square Meter) - Total Surface Area of Great Dodecahedron is the total quantity of plane enclosed on the entire surface of the Great Dodecahedron.
Edge Length of Great Dodecahedron - (Measured in Meter) - Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Great Dodecahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 15*sqrt(5-(2*sqrt(5)))*l_e^2 --> 15*sqrt(5-(2*sqrt(5)))*10^2

Evaluating ... ...

TSA = 1089.81379200804

STEP 3: Convert Result to Output's Unit

1089.81379200804 Square Meter --> No Conversion Required

FINAL ANSWER

1089.81379200804 ≈ 1089.814 Square Meter <-- Total Surface Area of Great Dodecahedron

(Calculation completed in 00.020 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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< 6 Surface Area of Great Dodecahedron Calculators

Total Surface Area of Great Dodecahedron given Surface to Volume Ratio

Go Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron))^2

Total Surface Area of Great Dodecahedron given Circumsphere Radius

Go Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^2

Total Surface Area of Great Dodecahedron given Pyramidal Height

Go Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^2

Total Surface Area of Great Dodecahedron given Volume

Go Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(2/3)

Total Surface Area of Great Dodecahedron given Ridge Length

Go Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^2

Total Surface Area of Great Dodecahedron

Go Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*Edge Length of Great Dodecahedron^2

Total Surface Area of Great Dodecahedron Formula

Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*Edge Length of Great Dodecahedron^2
TSA = 15*sqrt(5-(2*sqrt(5)))*l_e^2

What is Great Dodecahedron?

The Great Dodecahedron is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Total Surface Area of Great Dodecahedron?

Total Surface Area of Great Dodecahedron calculator uses Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*Edge Length of Great Dodecahedron^2 to calculate the Total Surface Area of Great Dodecahedron, Total Surface Area of Great Dodecahedron formula is defined as the total quantity of plane enclosed on the entire surface of the Great Dodecahedron. Total Surface Area of Great Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Dodecahedron using this online calculator? To use this online calculator for Total Surface Area of Great Dodecahedron, enter Edge Length of Great Dodecahedron (l_e) and hit the calculate button. Here is how the Total Surface Area of Great Dodecahedron calculation can be explained with given input values -> 1089.814 = 15*sqrt(5-(2*sqrt(5)))*10^2.

FAQ

What is Total Surface Area of Great Dodecahedron?

Total Surface Area of Great Dodecahedron formula is defined as the total quantity of plane enclosed on the entire surface of the Great Dodecahedron and is represented as TSA = 15*sqrt(5-(2*sqrt(5)))*l_e^2 or Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*Edge Length of Great Dodecahedron^2. Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.

How to calculate Total Surface Area of Great Dodecahedron?

Total Surface Area of Great Dodecahedron formula is defined as the total quantity of plane enclosed on the entire surface of the Great Dodecahedron is calculated using Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*Edge Length of Great Dodecahedron^2. To calculate Total Surface Area of Great Dodecahedron, you need Edge Length of Great Dodecahedron (l_e). With our tool, you need to enter the respective value for Edge Length of Great Dodecahedron 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 Dodecahedron?

In this formula, Total Surface Area of Great Dodecahedron uses Edge Length of Great Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^2
Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^2
Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^2
Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(2/3)
Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron))^2

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