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Pyramidal Height of Great Dodecahedron given Total Surface Area Formula

GoPyramidal Height of Great Dodecahedron Formula

GoPyramidal Height of Great Dodecahedron given Ridge Length Formula

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Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron. Check FAQs

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

h_Pyramid - Pyramidal Height of Great Dodecahedron?TSA - Total Surface Area of Great Dodecahedron?

Pyramidal Height of Great Dodecahedron given Total Surface Area Example

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Here is how the Pyramidal Height of Great Dodecahedron given Total Surface Area equation looks like with Values.

Here is how the Pyramidal Height of Great Dodecahedron given Total Surface Area equation looks like with Units.

Here is how the Pyramidal Height of Great Dodecahedron given Total Surface Area equation looks like.

2.2156 = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \sqrt{\frac{1100}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

2.2156m = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \sqrt{\frac{1100m²}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

2.2156 = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \sqrt{\frac{1100}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

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Pyramidal Height of Great Dodecahedron given Total Surface Area Solution

Follow our step by step solution on how to calculate Pyramidal Height of Great Dodecahedron given Total Surface Area?

FIRST Step Consider the formula

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \sqrt{\frac{TSA}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

Next Step Substitute values of Variables

∴

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \sqrt{\frac{1100m²}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

Next Step Prepare to Evaluate

∴

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \sqrt{\frac{1100}{15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})}}}

Next Step Evaluate

∴

h Pyramid = 2.21556392357366m

LAST Step Rounding Answer

∴

h Pyramid = 2.2156m

Pyramidal Height of Great Dodecahedron given Total Surface Area Formula Elements

Variables

Functions

Pyramidal Height of Great Dodecahedron

Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.

Symbol: h_Pyramid

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Pyramidal Height of Great Dodecahedron

Total Surface Area of Great Dodecahedron

Total Surface Area of Great Dodecahedron is the total quantity of plane enclosed on the entire surface of the Great Dodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Great Dodecahedron

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.

Syntax: sqrt(Number)

Other Formulas to find Pyramidal Height of Great Dodecahedron

Go Pyramidal Height of Great Dodecahedron

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot l e

Go Pyramidal Height of Great Dodecahedron given Ridge Length

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{2 \cdot l Ridge}{\sqrt{5} - 1}

Go Pyramidal Height of Great Dodecahedron given Circumsphere Radius

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot \frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}}

Go Pyramidal Height of Great Dodecahedron given Volume

h Pyramid = \frac{\sqrt{3} \cdot (3 - \sqrt{5})}{6} \cdot {(\frac{4 \cdot V}{5 \cdot (\sqrt{5} - 1)})}^{\frac{1}{3}}

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

Pyramidal Height of Great Dodecahedron given Total Surface Area evaluator 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 evaluate 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 evaluate Pyramidal Height of Great Dodecahedron given Total Surface Area using this online evaluator? To use this online evaluator for Pyramidal Height of Great Dodecahedron given Total Surface Area, enter Total Surface Area of Great Dodecahedron (TSA) and hit the calculate button.

FAQs on Pyramidal Height of Great Dodecahedron given Total Surface Area

What is the formula to find Pyramidal Height of Great Dodecahedron given Total Surface Area?

The formula of Pyramidal Height of Great Dodecahedron given Total Surface Area is expressed as Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5))))). Here is an example- 2.215564 = (sqrt(3)*(3-sqrt(5)))/6*sqrt(1100/(15*sqrt(5-(2*sqrt(5))))).

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

With Total Surface Area of Great Dodecahedron (TSA) we can find Pyramidal Height of Great Dodecahedron given Total Surface Area using the formula - Pyramidal Height of Great Dodecahedron = (sqrt(3)*(3-sqrt(5)))/6*sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5))))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Pyramidal Height of Great Dodecahedron?

Here are the different ways to Calculate Pyramidal Height of Great Dodecahedron-

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)))

Can the Pyramidal Height of Great Dodecahedron given Total Surface Area be negative?

No, the Pyramidal Height of Great Dodecahedron given Total Surface Area, measured in Length cannot be negative.

Which unit is used to measure Pyramidal Height of Great Dodecahedron given Total Surface Area?

Pyramidal Height of Great Dodecahedron given Total Surface Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Pyramidal Height of Great Dodecahedron given Total Surface Area can be measured.

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