Pyramidal Height of Great Dodecahedron given Total Surface Area Calculator

✖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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✖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 given Total Surface Area [h_Pyramid]

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Pyramidal Height of Great Dodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Great Dodecahedron: 1100 Square Meter --> 1100 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_Pyramid = (sqrt(3)*(3-sqrt(5)))/6*sqrt(TSA/(15*sqrt(5-(2*sqrt(5))))) --> (sqrt(3)*(3-sqrt(5)))/6*sqrt(1100/(15*sqrt(5-(2*sqrt(5)))))

Evaluating ... ...

h_Pyramid = 2.21556392357366

STEP 3: Convert Result to Output's Unit

2.21556392357366 Meter --> No Conversion Required

FINAL ANSWER

2.21556392357366 ≈ 2.215564 Meter <-- Pyramidal Height of Great Dodecahedron

(Calculation completed in 00.004 seconds)

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< Pyramidal Height of Great Dodecahedron Calculators

Pyramidal Height of Great Dodecahedron given Total Surface Area

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

Pyramidal Height of Great Dodecahedron given Circumsphere Radius

LaTeX Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5)))

Pyramidal Height of Great Dodecahedron given Ridge Length

LaTeX Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)

Pyramidal Height of Great Dodecahedron

LaTeX Go Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*Edge Length of Great Dodecahedron

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

Pyramidal Height of Great Dodecahedron given Total Surface Area calculator uses Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5))))) to calculate the Pyramidal Height of Great Dodecahedron, Pyramidal Height of Great Dodecahedron given Total Surface Area formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron, calculated using its total surface area. Pyramidal Height of Great Dodecahedron is denoted by h_Pyramid symbol.

How to calculate Pyramidal Height of Great Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Pyramidal Height of Great Dodecahedron given Total Surface Area, enter Total Surface Area of Great Dodecahedron (TSA) and hit the calculate button. Here is how the Pyramidal Height of Great Dodecahedron given Total Surface Area calculation can be explained with given input values -> 2.215564 = (sqrt(3)*(3-sqrt(5)))/6*sqrt(1100/(15*sqrt(5-(2*sqrt(5))))).

FAQ

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

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

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

Pyramidal Height of Great Dodecahedron given Total Surface Area formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron, calculated using its total surface area is calculated using Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5))))). To calculate Pyramidal Height of Great Dodecahedron given Total Surface Area, you need Total Surface Area of Great Dodecahedron (TSA). With our tool, you need to enter the respective value for Total Surface Area 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 Pyramidal Height of Great Dodecahedron?

In this formula, Pyramidal Height of Great Dodecahedron uses Total Surface Area of Great Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*Edge Length of Great Dodecahedron
Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)
Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*(4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5)))

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