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Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height Formula

GoTotal Surface Area of Great Stellated Dodecahedron Formula

GoTotal Surface Area of Great Stellated Dodecahedron given Ridge Length Formula

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Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron. Check FAQs

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

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

Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height Example

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

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

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

4546.4083 = 15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{6 \cdot 15}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

4546.4083m² = 15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{6 \cdot 15m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

4546.4083 = 15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{6 \cdot 15}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

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Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

TSA = 15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{6 \cdot 15m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{6 \cdot 15}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

Next Step Evaluate

∴

TSA = 4546.4082628683m²

LAST Step Rounding Answer

∴

TSA = 4546.4083m²

Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height Formula Elements

Variables

Functions

Total Surface Area of Great Stellated Dodecahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Great Stellated Dodecahedron

Pyramidal Height of Great Stellated Dodecahedron

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

Symbol: h_Pyramid

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Pyramidal Height of Great Stellated 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 Total Surface Area of Great Stellated Dodecahedron

Go Total Surface Area of Great Stellated Dodecahedron

TSA = 15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {l e}^{2}

Go Total Surface Area of Great Stellated Dodecahedron given Ridge Length

TSA = 15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot l Ridge}{1 + \sqrt{5}})}^{2}

Go Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord

TSA = 15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{l c(Pentagram)}{2 + \sqrt{5}})}^{2}

Go Total Surface Area of Great Stellated Dodecahedron given Circumradius

TSA = 15 \cdot \sqrt{5 + (2 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

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

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

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

FAQs on Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height

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

The formula of Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height is expressed as Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2. Here is an example- 4546.408 = 15*sqrt(5+(2*sqrt(5)))*((6*15)/(sqrt(3)*(3+sqrt(5))))^2.

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

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

What are the other ways to Calculate Total Surface Area of Great Stellated Dodecahedron?

Here are the different ways to Calculate Total Surface Area of Great Stellated Dodecahedron-

Total Surface Area of Great Stellated Dodecahedron=15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2
Total Surface Area of Great Stellated Dodecahedron=15*sqrt(5+(2*sqrt(5)))*((2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5)))^2
Total Surface Area of Great Stellated Dodecahedron=15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2

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

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

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

Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height can be measured.

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