Total Surface Area of Pentagonal Trapezohedron given Long Edge Calculator

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

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✖Total Surface Area of Pentagonal Trapezohedron is the total quantity of two dimensional space enclosed on the entire surface of the Pentagonal Trapezohedron.ⓘ Total Surface Area of Pentagonal Trapezohedron given Long Edge [TSA]

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Formula

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Total Surface Area of Pentagonal Trapezohedron given Long Edge

Formula

`"TSA" = (sqrt((25/2)*(5+sqrt(5))))*(("l"_{"e(Long)"}/(((sqrt(5)+1)/2)))^2)`

Example

`"929.9744m²"=(sqrt((25/2)*(5+sqrt(5))))*(("16m"/(((sqrt(5)+1)/2)))^2)`

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Total Surface Area of Pentagonal Trapezohedron given Long Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*((Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))^2)
TSA = (sqrt((25/2)*(5+sqrt(5))))*((l_e(Long)/(((sqrt(5)+1)/2)))^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

Total Surface Area of Pentagonal Trapezohedron - (Measured in Square Meter) - Total Surface Area of Pentagonal Trapezohedron is the total quantity of two dimensional space enclosed on the entire surface of the Pentagonal Trapezohedron.
Long Edge of Pentagonal Trapezohedron - (Measured in Meter) - Long Edge of Pentagonal Trapezohedron is the length of the any of the longer edges of the Pentagonal Trapezohedron.

STEP 1: Convert Input(s) to Base Unit

Long Edge of Pentagonal Trapezohedron: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (sqrt((25/2)*(5+sqrt(5))))*((l_e(Long)/(((sqrt(5)+1)/2)))^2) --> (sqrt((25/2)*(5+sqrt(5))))*((16/(((sqrt(5)+1)/2)))^2)

Evaluating ... ...

TSA = 929.974435846862

STEP 3: Convert Result to Output's Unit

929.974435846862 Square Meter --> No Conversion Required

FINAL ANSWER

929.974435846862 ≈ 929.9744 Square Meter <-- Total Surface Area of Pentagonal Trapezohedron

(Calculation completed in 00.004 seconds)

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< 6 Surface Area of Pentagonal Trapezohedron Calculators

Total Surface Area of Pentagonal Trapezohedron given Surface to Volume Ratio

Go Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*((((sqrt((25/2)*(5+sqrt(5)))))/((5/12)*(3+sqrt(5))*SA:V of Pentagonal Trapezohedron))^2)

Total Surface Area of Pentagonal Trapezohedron given Height

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

Total Surface Area of Pentagonal Trapezohedron given Volume

Go Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*((((12*Volume of Pentagonal Trapezohedron)/(5*(3+sqrt(5))))^(1/3))^2)

Total Surface Area of Pentagonal Trapezohedron given Short Edge

Go Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*((Short Edge of Pentagonal Trapezohedron/(((sqrt(5)-1)/2)))^2)

Total Surface Area of Pentagonal Trapezohedron given Long Edge

Go Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*((Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))^2)

Total Surface Area of Pentagonal Trapezohedron

Go Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*(Antiprism Edge Length of Pentagonal Trapezohedron^2)

Total Surface Area of Pentagonal Trapezohedron given Long Edge Formula

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 Total Surface Area of Pentagonal Trapezohedron given Long Edge?

Total Surface Area of Pentagonal Trapezohedron given Long Edge calculator uses Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*((Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))^2) to calculate the Total Surface Area of Pentagonal Trapezohedron, The Total Surface Area of Pentagonal Trapezohedron given Long Edge formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Pentagonal Trapezohedron, calculated using its long edge. Total Surface Area of Pentagonal Trapezohedron is denoted by TSA symbol.

How to calculate Total Surface Area of Pentagonal Trapezohedron given Long Edge using this online calculator? To use this online calculator for Total Surface Area of Pentagonal Trapezohedron given Long Edge, enter Long Edge of Pentagonal Trapezohedron (l_e(Long)) and hit the calculate button. Here is how the Total Surface Area of Pentagonal Trapezohedron given Long Edge calculation can be explained with given input values -> 929.9744 = (sqrt((25/2)*(5+sqrt(5))))*((16/(((sqrt(5)+1)/2)))^2).

FAQ

What is Total Surface Area of Pentagonal Trapezohedron given Long Edge?

The Total Surface Area of Pentagonal Trapezohedron given Long Edge formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Pentagonal Trapezohedron, calculated using its long edge and is represented as TSA = (sqrt((25/2)*(5+sqrt(5))))*((l_e(Long)/(((sqrt(5)+1)/2)))^2) or Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*((Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))^2). Long Edge of Pentagonal Trapezohedron is the length of the any of the longer edges of the Pentagonal Trapezohedron.

How to calculate Total Surface Area of Pentagonal Trapezohedron given Long Edge?

The Total Surface Area of Pentagonal Trapezohedron given Long Edge formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Pentagonal Trapezohedron, calculated using its long edge is calculated using Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*((Long Edge of Pentagonal Trapezohedron/(((sqrt(5)+1)/2)))^2). To calculate Total Surface Area of Pentagonal Trapezohedron given Long Edge, you need Long Edge of Pentagonal Trapezohedron (l_e(Long)). With our tool, you need to enter the respective value for Long 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 Total Surface Area of Pentagonal Trapezohedron?

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

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

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