Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Truncated Rhombohedron [r_c]

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✖Area of Pentagon of Truncated Rhombohedron is the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron.ⓘ Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius [A_Pentagon]

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Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2)
A_Pentagon = ((sqrt(5+(2*sqrt(5))))/4)*(((4*r_c)/(sqrt(14-(2*sqrt(5)))))^2)
This formula uses 1 Functions, 2 Variables

Functions Used

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., sqrt(Number)

Variables Used

Area of Pentagon of Truncated Rhombohedron - (Measured in Square Meter) - Area of Pentagon of Truncated Rhombohedron is the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron.
Circumsphere Radius of Truncated Rhombohedron - (Measured in Meter) - Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Truncated Rhombohedron: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Pentagon = ((sqrt(5+(2*sqrt(5))))/4)*(((4*r_c)/(sqrt(14-(2*sqrt(5)))))^2) --> ((sqrt(5+(2*sqrt(5))))/4)*(((4*20)/(sqrt(14-(2*sqrt(5)))))^2)

Evaluating ... ...

A_Pentagon = 516.830806592412

STEP 3: Convert Result to Output's Unit

516.830806592412 Square Meter --> No Conversion Required

FINAL ANSWER

516.830806592412 ≈ 516.8308 Square Meter <-- Area of Pentagon of Truncated Rhombohedron

(Calculation completed in 00.004 seconds)

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< Area of Pentagon of Truncated Rhombohedron Calculators

Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius

LaTeX Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2)

Area of Pentagon of Truncated Rhombohedron given Triangular Edge Length

LaTeX Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*((Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))^2)

Area of Pentagon of Truncated Rhombohedron

LaTeX Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2)

Area of Pentagon of Truncated Rhombohedron given Rhombohedral Edge Length

LaTeX Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(Rhombohedral Edge Length of Truncated Rhombohedron^2)

Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius Formula

LaTeX Go

What is Truncated Rhombohedron?

The Truncated Rhombohedron is a convex, octahedral polyhedron. It is made up of six equal, irregular, but axially symmetrical pentagons and two equilateral triangles. It has twelve corners; three faces meet at each corner (a triangle and two pentagons or three pentagons). All corner points lie on the same sphere. Opposite faces are parallel. In the stitch, the body stands on a triangular surface, the pentagons virtually form the surface. The number of edges is eighteen.

How to Calculate Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius?

Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius calculator uses Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2) to calculate the Area of Pentagon of Truncated Rhombohedron, Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius formula is defined as the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron, calculated using its circumsphere radius. Area of Pentagon of Truncated Rhombohedron is denoted by A_Pentagon symbol.

How to calculate Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius using this online calculator? To use this online calculator for Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius, enter Circumsphere Radius of Truncated Rhombohedron (r_c) and hit the calculate button. Here is how the Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius calculation can be explained with given input values -> 516.8308 = ((sqrt(5+(2*sqrt(5))))/4)*(((4*20)/(sqrt(14-(2*sqrt(5)))))^2).

FAQ

What is Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius?

Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius formula is defined as the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron, calculated using its circumsphere radius and is represented as A_Pentagon = ((sqrt(5+(2*sqrt(5))))/4)*(((4*r_c)/(sqrt(14-(2*sqrt(5)))))^2) or Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2). Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.

How to calculate Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius?

Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius formula is defined as the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron, calculated using its circumsphere radius is calculated using Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2). To calculate Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius, you need Circumsphere Radius of Truncated Rhombohedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Truncated Rhombohedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Area of Pentagon of Truncated Rhombohedron?

In this formula, Area of Pentagon of Truncated Rhombohedron uses Circumsphere Radius of Truncated Rhombohedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(Rhombohedral Edge Length of Truncated Rhombohedron^2)
Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2)
Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*((Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))^2)

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