Total Surface Area of Great Dodecahedron given Pyramidal Height Calculator

✖Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.ⓘ Pyramidal Height of Great Dodecahedron [h_Pyramid]

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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 Pyramidal Height [TSA]

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Total Surface Area of Great Dodecahedron given Pyramidal Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^2
TSA = 15*sqrt(5-(2*sqrt(5)))*((6*h_Pyramid)/(sqrt(3)*(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 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.
Pyramidal Height of Great Dodecahedron - (Measured in Meter) - Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pyramidal Height of Great Dodecahedron: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 15*sqrt(5-(2*sqrt(5)))*((6*h_Pyramid)/(sqrt(3)*(3-sqrt(5))))^2 --> 15*sqrt(5-(2*sqrt(5)))*((6*2)/(sqrt(3)*(3-sqrt(5))))^2

Evaluating ... ...

TSA = 896.363382557801

STEP 3: Convert Result to Output's Unit

896.363382557801 Square Meter --> No Conversion Required

FINAL ANSWER

896.363382557801 ≈ 896.3634 Square Meter <-- Total Surface Area of Great Dodecahedron

(Calculation completed in 00.004 seconds)

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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 Pyramidal Height Formula

LaTeX Go

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 Pyramidal Height?

Total Surface Area of Great Dodecahedron given Pyramidal Height calculator uses Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^2 to calculate the Total Surface Area of Great Dodecahedron, Total Surface Area of Great Dodecahedron given Pyramidal Height formula is defined as the total quantity of plane enclosed on the entire surface of the Great Dodecahedron, calculated using its pyramidal height. Total Surface Area of Great Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Dodecahedron given Pyramidal Height using this online calculator? To use this online calculator for Total Surface Area of Great Dodecahedron given Pyramidal Height, enter Pyramidal Height of Great Dodecahedron (h_Pyramid) and hit the calculate button. Here is how the Total Surface Area of Great Dodecahedron given Pyramidal Height calculation can be explained with given input values -> 896.3634 = 15*sqrt(5-(2*sqrt(5)))*((6*2)/(sqrt(3)*(3-sqrt(5))))^2.

FAQ

What is Total Surface Area of Great Dodecahedron given Pyramidal Height?

Total Surface Area of Great Dodecahedron given Pyramidal Height formula is defined as the total quantity of plane enclosed on the entire surface of the Great Dodecahedron, calculated using its pyramidal height and is represented as TSA = 15*sqrt(5-(2*sqrt(5)))*((6*h_Pyramid)/(sqrt(3)*(3-sqrt(5))))^2 or Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^2. Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.

How to calculate Total Surface Area of Great Dodecahedron given Pyramidal Height?

Total Surface Area of Great Dodecahedron given Pyramidal Height formula is defined as the total quantity of plane enclosed on the entire surface of the Great Dodecahedron, calculated using its pyramidal height is calculated using Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^2. To calculate Total Surface Area of Great Dodecahedron given Pyramidal Height, you need Pyramidal Height of Great Dodecahedron (h_Pyramid). With our tool, you need to enter the respective value for Pyramidal Height 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 Pyramidal Height 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)))*((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

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