Area of Pentagon of Truncated Rhombohedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2)
APentagon = ((sqrt(5+(2*sqrt(5))))/4)*(((2*le)/(3-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.
Edge Length of Truncated Rhombohedron - (Measured in Meter) - Edge Length of Truncated Rhombohedron is the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Truncated Rhombohedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
APentagon = ((sqrt(5+(2*sqrt(5))))/4)*(((2*le)/(3-sqrt(5)))^2) --> ((sqrt(5+(2*sqrt(5))))/4)*(((2*10)/(3-sqrt(5)))^2)
Evaluating ... ...
APentagon = 527.36891959118
STEP 3: Convert Result to Output's Unit
527.36891959118 Square Meter --> No Conversion Required
FINAL ANSWER
527.36891959118 527.3689 Square Meter <-- Area of Pentagon of Truncated Rhombohedron
(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli
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7 Area of Pentagon of Truncated Rhombohedron Calculators

Area of Pentagon of Truncated Rhombohedron given Surface to Volume Ratio
Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*(5/3)*(sqrt(sqrt(5)-2))*Surface to Volume Ratio of Truncated Rhombohedron))^2)
Area of Pentagon of Truncated Rhombohedron given Total Surface Area
Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*((2*Total Surface Area of Truncated Rhombohedron)/((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15))))
Area of Pentagon of Truncated Rhombohedron given Circumsphere Radius
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
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 given Volume
Go Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((3*Volume of Truncated Rhombohedron)/(5*(sqrt(sqrt(5)-2))))^(2/3))
Area of Pentagon of Truncated Rhombohedron
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
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 Formula

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

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?

Area of Pentagon of Truncated Rhombohedron calculator uses Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2) to calculate the Area of Pentagon of Truncated Rhombohedron, Area of Pentagon of Truncated Rhombohedron formula is defined as the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron. Area of Pentagon of Truncated Rhombohedron is denoted by APentagon symbol.

How to calculate Area of Pentagon of Truncated Rhombohedron using this online calculator? To use this online calculator for Area of Pentagon of Truncated Rhombohedron, enter Edge Length of Truncated Rhombohedron (le) and hit the calculate button. Here is how the Area of Pentagon of Truncated Rhombohedron calculation can be explained with given input values -> 527.3689 = ((sqrt(5+(2*sqrt(5))))/4)*(((2*10)/(3-sqrt(5)))^2).

FAQ

What is Area of Pentagon of Truncated Rhombohedron?
Area of Pentagon of Truncated Rhombohedron formula is defined as the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron and is represented as APentagon = ((sqrt(5+(2*sqrt(5))))/4)*(((2*le)/(3-sqrt(5)))^2) or Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2). Edge Length of Truncated Rhombohedron is the length of the edge that joins the triangular edge with rhombohedral edges on each face of the Truncated Rhombohedron.
How to calculate Area of Pentagon of Truncated Rhombohedron?
Area of Pentagon of Truncated Rhombohedron formula is defined as the total quantity of two dimensional space enclosed on any pentagonal face of the Truncated Rhombohedron is calculated using Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2). To calculate Area of Pentagon of Truncated Rhombohedron, you need Edge Length of Truncated Rhombohedron (le). With our tool, you need to enter the respective value for Edge Length 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 Edge Length of Truncated Rhombohedron. We can use 6 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)*((Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))^2)
  • 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 = ((sqrt(5+(2*sqrt(5))))/4)*((2*Total Surface Area of Truncated Rhombohedron)/((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15))))
  • Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*(((3*Volume of Truncated Rhombohedron)/(5*(sqrt(sqrt(5)-2))))^(2/3))
  • Area of Pentagon of Truncated Rhombohedron = ((sqrt(5+(2*sqrt(5))))/4)*((((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/(2*(5/3)*(sqrt(sqrt(5)-2))*Surface to Volume Ratio of Truncated Rhombohedron))^2)
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