Height of Pentagonal Trapezohedron given Short Edge Calculator

✖Short Edge of Pentagonal Trapezohedron is the length of any of the shorter edges of the Pentagonal Trapezohedron.ⓘ Short Edge of Pentagonal Trapezohedron [l_e(Short)]

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✖Height of Pentagonal Trapezohedron is the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join.ⓘ Height of Pentagonal Trapezohedron given Short Edge [h]

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Formula

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Height of Pentagonal Trapezohedron given Short Edge

Formula

`"h" = (sqrt(5+2*sqrt(5)))*("l"_{"e(Short)"}/(((sqrt(5)-1)/2)))`

Example

`"29.87878m"=(sqrt(5+2*sqrt(5)))*("6m"/(((sqrt(5)-1)/2)))`

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Height of Pentagonal Trapezohedron given Short Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2)))
h = (sqrt(5+2*sqrt(5)))*(l_e(Short)/(((sqrt(5)-1)/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

Height of Pentagonal Trapezohedron - (Measured in Meter) - Height of Pentagonal Trapezohedron is the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join.
Short Edge of Pentagonal Trapezohedron - (Measured in Meter) - Short Edge of Pentagonal Trapezohedron is the length of any of the shorter edges of the Pentagonal Trapezohedron.

STEP 1: Convert Input(s) to Base Unit

Short Edge of Pentagonal Trapezohedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (sqrt(5+2*sqrt(5)))*(l_e(Short)/(((sqrt(5)-1)/2))) --> (sqrt(5+2*sqrt(5)))*(6/(((sqrt(5)-1)/2)))

Evaluating ... ...

h = 29.8787794185934

STEP 3: Convert Result to Output's Unit

29.8787794185934 Meter --> No Conversion Required

FINAL ANSWER

29.8787794185934 ≈ 29.87878 Meter <-- Height of Pentagonal Trapezohedron

(Calculation completed in 00.004 seconds)

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< 6 Height of Pentagonal Trapezohedron Calculators

Height of Pentagonal Trapezohedron given Surface to Volume Ratio

Go Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*SA:V of Pentagonal Trapezohedron))

Height of Pentagonal Trapezohedron given Total Surface Area

Go Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(sqrt(Total Surface Area of Pentagonal Trapezohedron/((sqrt((25/2)*(5+sqrt(5)))))))

Height of Pentagonal Trapezohedron given Volume

Go Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(((12*Volume of Pentagonal Trapezohedron)/(5*(3+sqrt(5))))^(1/3))

Height of Pentagonal Trapezohedron given Short Edge

Go Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2)))

Height of Pentagonal Trapezohedron given Long Edge

Go Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))

Height of Pentagonal Trapezohedron

Go Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*Antiprism Edge Length of Pentagonal Trapezohedron

Height of Pentagonal Trapezohedron given Short Edge Formula

Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2)))
h = (sqrt(5+2*sqrt(5)))*(l_e(Short)/(((sqrt(5)-1)/2)))

What is a Pentagonal Trapezohedron?

In geometry, a Pentagonal Trapezohedron or deltohedron is the third in an infinite series of face-transitive polyhedra which are dual polyhedra to the antiprisms. It has ten faces (i.e., it is a decahedron) which are congruent kites. It can be decomposed into two pentagonal pyramids and a pentagonal antiprism in the middle. It can also be decomposed into two pentagonal pyramids and a dodecahedron in the middle.

What is a Trapezohedron?

The n-gonal Trapezohedron, antidipyramid, antibipyramid, or deltohedron is the dual polyhedron of an n-gonal antiprism. The 2n faces of the n-trapezohedron are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its 2n faces are kites (also called deltoids). The n-gon part of the name does not refer to faces here but to two arrangements of vertices around an axis of symmetry. The dual n-gonal antiprism has two actual n-gon faces. An n-gonal trapezohedron can be dissected into two equal n-gonal pyramids and an n-gonal antiprism.

How to Calculate Height of Pentagonal Trapezohedron given Short Edge?

Height of Pentagonal Trapezohedron given Short Edge calculator uses Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2))) to calculate the Height of Pentagonal Trapezohedron, The Height of Pentagonal Trapezohedron given Short Edge formula is defined as the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join, calculated using its short edge. Height of Pentagonal Trapezohedron is denoted by h symbol.

How to calculate Height of Pentagonal Trapezohedron given Short Edge using this online calculator? To use this online calculator for Height of Pentagonal Trapezohedron given Short Edge, enter Short Edge of Pentagonal Trapezohedron (l_e(Short)) and hit the calculate button. Here is how the Height of Pentagonal Trapezohedron given Short Edge calculation can be explained with given input values -> 29.87878 = (sqrt(5+2*sqrt(5)))*(6/(((sqrt(5)-1)/2))).

FAQ

What is Height of Pentagonal Trapezohedron given Short Edge?

The Height of Pentagonal Trapezohedron given Short Edge formula is defined as the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join, calculated using its short edge and is represented as h = (sqrt(5+2*sqrt(5)))*(l_e(Short)/(((sqrt(5)-1)/2))) or Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2))). Short Edge of Pentagonal Trapezohedron is the length of any of the shorter edges of the Pentagonal Trapezohedron.

How to calculate Height of Pentagonal Trapezohedron given Short Edge?

The Height of Pentagonal Trapezohedron given Short Edge formula is defined as the distance between two peak vertices where long edges of the Pentagonal Trapezohedron join, calculated using its short edge is calculated using Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2))). To calculate Height of Pentagonal Trapezohedron given Short Edge, you need Short Edge of Pentagonal Trapezohedron (l_e(Short)). With our tool, you need to enter the respective value for Short Edge of Pentagonal Trapezohedron 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 Height of Pentagonal Trapezohedron?

In this formula, Height of Pentagonal Trapezohedron uses Short Edge of Pentagonal Trapezohedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*Antiprism Edge Length of Pentagonal Trapezohedron
Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))
Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(sqrt(Total Surface Area of Pentagonal Trapezohedron/((sqrt((25/2)*(5+sqrt(5)))))))
Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(((12*Volume of Pentagonal Trapezohedron)/(5*(3+sqrt(5))))^(1/3))
Height of Pentagonal Trapezohedron = (sqrt(5+2*sqrt(5)))*(((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*SA:V of Pentagonal Trapezohedron))

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