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Total Surface Area of Dodecahedron given Space Diagonal Formula

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GoTotal Surface Area of Dodecahedron given Volume Formula

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

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d Space}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

TSA - Total Surface Area of Dodecahedron?d_Space - Space Diagonal of Dodecahedron?

Total Surface Area of Dodecahedron given Space Diagonal Example

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Here is how the Total Surface Area of Dodecahedron given Space Diagonal equation looks like with Values.

Here is how the Total Surface Area of Dodecahedron given Space Diagonal equation looks like with Units.

Here is how the Total Surface Area of Dodecahedron given Space Diagonal equation looks like.

2060.866 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

2060.866m² = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

2060.866 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

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Total Surface Area of Dodecahedron given Space Diagonal Solution

Follow our step by step solution on how to calculate Total Surface Area of Dodecahedron given Space Diagonal?

FIRST Step Consider the formula

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d Space}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Substitute values of Variables

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 28}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Evaluate

∴

TSA = 2060.865959507m²

LAST Step Rounding Answer

∴

TSA = 2060.866m²

Total Surface Area of Dodecahedron given Space Diagonal Formula Elements

Variables

Functions

Total Surface Area of Dodecahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Dodecahedron

Space Diagonal of Dodecahedron

The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.

Symbol: d_Space

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Space Diagonal of 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 Dodecahedron

Go Total Surface Area of Dodecahedron

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {l e}^{2}

Go Total Surface Area of Dodecahedron given Volume

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{2}{3}}

Go Total Surface Area of Dodecahedron given Face Diagonal

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d Face}{1 + \sqrt{5}})}^{2}

Go Total Surface Area of Dodecahedron given Circumsphere Radius

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

How to Evaluate Total Surface Area of Dodecahedron given Space Diagonal?

Total Surface Area of Dodecahedron given Space Diagonal evaluator uses Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2 to evaluate the Total Surface Area of Dodecahedron, The Total Surface Area of Dodecahedron given Space Diagonal formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using space diagonal of Dodecahedron. Total Surface Area of Dodecahedron is denoted by TSA symbol.

How to evaluate Total Surface Area of Dodecahedron given Space Diagonal using this online evaluator? To use this online evaluator for Total Surface Area of Dodecahedron given Space Diagonal, enter Space Diagonal of Dodecahedron (d_Space) and hit the calculate button.

FAQs on Total Surface Area of Dodecahedron given Space Diagonal

What is the formula to find Total Surface Area of Dodecahedron given Space Diagonal?

The formula of Total Surface Area of Dodecahedron given Space Diagonal is expressed as Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. Here is an example- 2060.866 = 3*sqrt(25+(10*sqrt(5)))*((2*28)/(sqrt(3)*(1+sqrt(5))))^2.

How to calculate Total Surface Area of Dodecahedron given Space Diagonal?

With Space Diagonal of Dodecahedron (d_Space) we can find Total Surface Area of Dodecahedron given Space Diagonal using the formula - Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Total Surface Area of Dodecahedron=3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Total Surface Area of Dodecahedron=3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
Total Surface Area of Dodecahedron=3*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2

Can the Total Surface Area of Dodecahedron given Space Diagonal be negative?

No, the Total Surface Area of Dodecahedron given Space Diagonal, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Dodecahedron given Space Diagonal?

Total Surface Area of Dodecahedron given Space Diagonal 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 Dodecahedron given Space Diagonal can be measured.

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