Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area Calculator

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

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✖Pyramidal Height of Great Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.ⓘ Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area [h_Pyramid]

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Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*sqrt(Total Surface Area of Great Stellated 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 Stellated Dodecahedron - (Measured in Meter) - Pyramidal Height of Great Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Stellated Dodecahedron.
Total Surface Area of Great Stellated Dodecahedron - (Measured in Square Meter) - Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Great Stellated Dodecahedron: 4600 Square Meter --> 4600 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(4600/(15*sqrt(5+(2*sqrt(5)))))

Evaluating ... ...

h_Pyramid = 15.0881488096429

STEP 3: Convert Result to Output's Unit

15.0881488096429 Meter --> No Conversion Required

FINAL ANSWER

15.0881488096429 ≈ 15.08815 Meter <-- Pyramidal Height of Great Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< Pyramidal Height of Great Stellated Dodecahedron Calculators

Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area

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

Pyramidal Height of Great Stellated Dodecahedron given Ridge Length

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

Pyramidal Height of Great Stellated Dodecahedron given Pentagram Chord

LaTeX Go Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))

Pyramidal Height of Great Stellated Dodecahedron

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

Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area Formula

LaTeX Go

What is Great Stellated Dodecahedron?

The Great Stellated Dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {⁵⁄₂,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.

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

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

How to calculate Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area using this online calculator? To use this online calculator for Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area, enter Total Surface Area of Great Stellated Dodecahedron (TSA) and hit the calculate button. Here is how the Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area calculation can be explained with given input values -> 15.08815 = (sqrt(3)*(3+sqrt(5)))/6*sqrt(4600/(15*sqrt(5+(2*sqrt(5))))).

FAQ

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

Pyramidal Height of Great Stellated Dodecahedron given Total Surface Area formula is defined as the height of any of the inwards directed tetrahedral pyramids of the Great Stellated 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 Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*sqrt(Total Surface Area of Great Stellated Dodecahedron/(15*sqrt(5+(2*sqrt(5))))). Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.

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

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

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

Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*Edge Length of Great Stellated Dodecahedron
Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*(2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5))
Pyramidal Height of Great Stellated Dodecahedron = (sqrt(3)*(3+sqrt(5)))/6*Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5))

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