FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Face Area of Dodecahedron given Midsphere Radius Formula

GoFace Area of Dodecahedron Formula

Fx Copy

LaTeX Copy

The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron. Check FAQs

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r m}{3 + \sqrt{5}})}^{2}

A_Face - Face Area of Dodecahedron?r_m - Midsphere Radius of Dodecahedron?

Face Area of Dodecahedron given Midsphere Radius Example

With values

With units

Only example

Here is how the Face Area of Dodecahedron given Midsphere Radius equation looks like with Values.

Here is how the Face Area of Dodecahedron given Midsphere Radius equation looks like with Units.

Here is how the Face Area of Dodecahedron given Midsphere Radius equation looks like.

169.6856 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13}{3 + \sqrt{5}})}^{2}

169.6856m² = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13m}{3 + \sqrt{5}})}^{2}

169.6856 = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13}{3 + \sqrt{5}})}^{2}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

3D Geometry » fx Face Area of Dodecahedron given Midsphere Radius

Face Area of Dodecahedron given Midsphere Radius Solution

Follow our step by step solution on how to calculate Face Area of Dodecahedron given Midsphere Radius?

FIRST Step Consider the formula

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r m}{3 + \sqrt{5}})}^{2}

Next Step Substitute values of Variables

∴

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13m}{3 + \sqrt{5}})}^{2}

Next Step Prepare to Evaluate

∴

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 13}{3 + \sqrt{5}})}^{2}

Next Step Evaluate

∴

A Face = 169.685646423862m²

LAST Step Rounding Answer

∴

A Face = 169.6856m²

Face Area of Dodecahedron given Midsphere Radius Formula Elements

Variables

Functions

Face Area of Dodecahedron

The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron.

Symbol: A_Face

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Face Area of Dodecahedron

Midsphere Radius of Dodecahedron

The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere Radius 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 Face Area of Dodecahedron

Go Face Area of Dodecahedron

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {l e}^{2}

Other formulas in Face Area of Dodecahedron category

Go Lateral Surface Area of Dodecahedron

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

Go Lateral Surface Area of Dodecahedron given Total Surface Area

LSA = \frac{5}{6} \cdot TSA

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}}

How to Evaluate Face Area of Dodecahedron given Midsphere Radius?

Face Area of Dodecahedron given Midsphere Radius evaluator uses Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2 to evaluate the Face Area of Dodecahedron, The Face Area of Dodecahedron given Midsphere Radius formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using midsphere radius of Dodecahedron. Face Area of Dodecahedron is denoted by A_Face symbol.

How to evaluate Face Area of Dodecahedron given Midsphere Radius using this online evaluator? To use this online evaluator for Face Area of Dodecahedron given Midsphere Radius, enter Midsphere Radius of Dodecahedron (r_m) and hit the calculate button.

FAQs on Face Area of Dodecahedron given Midsphere Radius

What is the formula to find Face Area of Dodecahedron given Midsphere Radius?

The formula of Face Area of Dodecahedron given Midsphere Radius is expressed as Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2. Here is an example- 169.6856 = 1/4*sqrt(25+(10*sqrt(5)))*((4*13)/(3+sqrt(5)))^2.

How to calculate Face Area of Dodecahedron given Midsphere Radius?

With Midsphere Radius of Dodecahedron (r_m) we can find Face Area of Dodecahedron given Midsphere Radius using the formula - Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Face Area of Dodecahedron?

Here are the different ways to Calculate Face Area of Dodecahedron-

Face Area of Dodecahedron=1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2

Can the Face Area of Dodecahedron given Midsphere Radius be negative?

No, the Face Area of Dodecahedron given Midsphere Radius, measured in Area cannot be negative.

Which unit is used to measure Face Area of Dodecahedron given Midsphere Radius?

Face Area of Dodecahedron given Midsphere Radius 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 Face Area of Dodecahedron given Midsphere Radius can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit