Total Surface Area of Great Dodecahedron given Ridge Length Calculator

✖Ridge Length of Great Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Dodecahedron.ⓘ Ridge Length of Great Dodecahedron [l_Ridge]

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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 given Ridge Length [TSA]

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Total Surface Area of Great Dodecahedron given Ridge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^2
TSA = 15*sqrt(5-(2*sqrt(5)))*((2*l_Ridge)/(sqrt(5)-1))^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.
Ridge Length of Great Dodecahedron - (Measured in Meter) - Ridge Length of Great Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Ridge Length of Great Dodecahedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 15*sqrt(5-(2*sqrt(5)))*((2*l_Ridge)/(sqrt(5)-1))^2 --> 15*sqrt(5-(2*sqrt(5)))*((2*6)/(sqrt(5)-1))^2

Evaluating ... ...

TSA = 1027.14103759877

STEP 3: Convert Result to Output's Unit

1027.14103759877 Square Meter --> No Conversion Required

FINAL ANSWER

1027.14103759877 ≈ 1027.141 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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Indian Institute of Information Technology (IIIT), Bhopal

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< Surface Area of Great Dodecahedron Calculators

Total Surface Area of Great Dodecahedron given Circumsphere Radius

LaTeX 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

LaTeX 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 Ridge Length

LaTeX 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

LaTeX 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 given Ridge Length Formula

LaTeX Go

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

Total Surface Area of Great Dodecahedron given Ridge Length calculator uses Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^2 to calculate the Total Surface Area of Great Dodecahedron, Total Surface Area of Great Dodecahedron given Ridge Length formula is defined as the total quantity of plane enclosed on the entire surface of the Great Dodecahedron, calculated using its ridge length. Total Surface Area of Great Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Dodecahedron given Ridge Length using this online calculator? To use this online calculator for Total Surface Area of Great Dodecahedron given Ridge Length, enter Ridge Length of Great Dodecahedron (l_Ridge) and hit the calculate button. Here is how the Total Surface Area of Great Dodecahedron given Ridge Length calculation can be explained with given input values -> 1027.141 = 15*sqrt(5-(2*sqrt(5)))*((2*6)/(sqrt(5)-1))^2.

FAQ

What is Total Surface Area of Great Dodecahedron given Ridge Length?

Total Surface Area of Great Dodecahedron given Ridge Length formula is defined as the total quantity of plane enclosed on the entire surface of the Great Dodecahedron, calculated using its ridge length and is represented as TSA = 15*sqrt(5-(2*sqrt(5)))*((2*l_Ridge)/(sqrt(5)-1))^2 or Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^2. Ridge Length of Great Dodecahedron is the distance between any inwards directed pyramidal apex and any of its adjacent peak vertex of the Great Dodecahedron.

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

Total Surface Area of Great Dodecahedron given Ridge Length formula is defined as the total quantity of plane enclosed on the entire surface of the Great Dodecahedron, calculated using its ridge length is calculated using Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^2. To calculate Total Surface Area of Great Dodecahedron given Ridge Length, you need Ridge Length of Great Dodecahedron (l_Ridge). With our tool, you need to enter the respective value for Ridge 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 Ridge Length of Great Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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