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Total Surface Area of Dodecahedron given Face Diagonal Formula

GoTotal Surface Area of Dodecahedron Formula

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 Face}{1 + \sqrt{5}})}^{2}

TSA - Total Surface Area of Dodecahedron?d_Face - Face Diagonal of Dodecahedron?

Total Surface Area of Dodecahedron given Face Diagonal Example

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

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

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

2018.8075 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{2}

2018.8075m² = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16m}{1 + \sqrt{5}})}^{2}

2018.8075 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{2}

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Total Surface Area of Dodecahedron given Face Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16m}{1 + \sqrt{5}})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 16}{1 + \sqrt{5}})}^{2}

Next Step Evaluate

∴

TSA = 2018.80747053747m²

LAST Step Rounding Answer

∴

TSA = 2018.8075m²

Total Surface Area of Dodecahedron given Face 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

Face Diagonal of Dodecahedron

The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.

Symbol: d_Face

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Face 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 Circumsphere Radius

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

Go Total Surface Area of Dodecahedron given Face Area

TSA = 12 \cdot A Face

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

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

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

FAQs on Total Surface Area of Dodecahedron given Face Diagonal

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

The formula of Total Surface Area of Dodecahedron given Face Diagonal is expressed as Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2. Here is an example- 2018.807 = 3*sqrt(25+(10*sqrt(5)))*((2*16)/(1+sqrt(5)))^2.

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

With Face Diagonal of Dodecahedron (d_Face) we can find Total Surface Area of Dodecahedron given Face Diagonal using the formula - Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(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)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2

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

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

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

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

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