Total Surface Area of Tetragonal Trapezohedron Calculator

✖Antiprism Edge Length of Tetragonal Trapezohedron is the distance between any pair of adjacent vertices of the antiprism which corresponds to the Tetragonal Trapezohedron.ⓘ Antiprism Edge Length of Tetragonal Trapezohedron [l_e(Antiprism)]

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✖Total Surface Area of Tetragonal Trapezohedron is the total quantity of two-dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron.ⓘ Total Surface Area of Tetragonal Trapezohedron [TSA]

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Formula

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Total Surface Area of Tetragonal Trapezohedron

Formula

`"TSA" = 2*sqrt(2+4*sqrt(2))*("l"_{"e(Antiprism)"}^2)`

Example

`"553.4204m²"=2*sqrt(2+4*sqrt(2))*(("10m")^2)`

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Total Surface Area of Tetragonal Trapezohedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(Antiprism Edge Length of Tetragonal Trapezohedron^2)
TSA = 2*sqrt(2+4*sqrt(2))*(l_e(Antiprism)^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 Tetragonal Trapezohedron - (Measured in Square Meter) - Total Surface Area of Tetragonal Trapezohedron is the total quantity of two-dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron.
Antiprism Edge Length of Tetragonal Trapezohedron - (Measured in Meter) - Antiprism Edge Length of Tetragonal Trapezohedron is the distance between any pair of adjacent vertices of the antiprism which corresponds to the Tetragonal Trapezohedron.

STEP 1: Convert Input(s) to Base Unit

Antiprism Edge Length of Tetragonal Trapezohedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 2*sqrt(2+4*sqrt(2))*(l_e(Antiprism)^2) --> 2*sqrt(2+4*sqrt(2))*(10^2)

Evaluating ... ...

TSA = 553.420427866279

STEP 3: Convert Result to Output's Unit

553.420427866279 Square Meter --> No Conversion Required

FINAL ANSWER

553.420427866279 ≈ 553.4204 Square Meter <-- Total Surface Area of Tetragonal Trapezohedron

(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru

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Indian Institute of Information Technology (IIIT), Bhopal

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< 6 Total Surface Area of Tetragonal Trapezohedron Calculators

Total Surface Area of Tetragonal Trapezohedron given Surface to Volume Ratio

Go Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(((2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*SA:V of Tetragonal Trapezohedron))^2)

Total Surface Area of Tetragonal Trapezohedron given Volume

Go Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((((3*Volume of Tetragonal Trapezohedron)/(sqrt(4+3*sqrt(2))))^(1/3))^2)

Total Surface Area of Tetragonal Trapezohedron given Long Edge

Go Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(((2*Long Edge of Tetragonal Trapezohedron)/(sqrt(2*(1+sqrt(2)))))^2)

Total Surface Area of Tetragonal Trapezohedron given Height

Go Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^2)

Total Surface Area of Tetragonal Trapezohedron given Short Edge

Go Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))^2)

Total Surface Area of Tetragonal Trapezohedron

Go Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(Antiprism Edge Length of Tetragonal Trapezohedron^2)

Total Surface Area of Tetragonal Trapezohedron Formula

Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(Antiprism Edge Length of Tetragonal Trapezohedron^2)
TSA = 2*sqrt(2+4*sqrt(2))*(l_e(Antiprism)^2)

What is a Tetragonal Trapezohedron?

In geometry, a Tetragonal Trapezohedron, or deltohedron, is the second in an infinite series of trapezohedra, which are dual to the antiprisms. It has eight faces, which are congruent kites, and is dual to the square antiprism.

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 Tetragonal Trapezohedron?

Total Surface Area of Tetragonal Trapezohedron calculator uses Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(Antiprism Edge Length of Tetragonal Trapezohedron^2) to calculate the Total Surface Area of Tetragonal Trapezohedron, The Total Surface Area of Tetragonal Trapezohedron formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron. Total Surface Area of Tetragonal Trapezohedron is denoted by TSA symbol.

How to calculate Total Surface Area of Tetragonal Trapezohedron using this online calculator? To use this online calculator for Total Surface Area of Tetragonal Trapezohedron, enter Antiprism Edge Length of Tetragonal Trapezohedron (l_e(Antiprism)) and hit the calculate button. Here is how the Total Surface Area of Tetragonal Trapezohedron calculation can be explained with given input values -> 553.4204 = 2*sqrt(2+4*sqrt(2))*(10^2).

FAQ

What is Total Surface Area of Tetragonal Trapezohedron?

The Total Surface Area of Tetragonal Trapezohedron formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron and is represented as TSA = 2*sqrt(2+4*sqrt(2))*(l_e(Antiprism)^2) or Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(Antiprism Edge Length of Tetragonal Trapezohedron^2). Antiprism Edge Length of Tetragonal Trapezohedron is the distance between any pair of adjacent vertices of the antiprism which corresponds to the Tetragonal Trapezohedron.

How to calculate Total Surface Area of Tetragonal Trapezohedron?

The Total Surface Area of Tetragonal Trapezohedron formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron is calculated using Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(Antiprism Edge Length of Tetragonal Trapezohedron^2). To calculate Total Surface Area of Tetragonal Trapezohedron, you need Antiprism Edge Length of Tetragonal Trapezohedron (l_e(Antiprism)). With our tool, you need to enter the respective value for Antiprism Edge Length of Tetragonal 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 Tetragonal Trapezohedron?

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

Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^2)
Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(((2*Long Edge of Tetragonal Trapezohedron)/(sqrt(2*(1+sqrt(2)))))^2)
Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))^2)
Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*(((2*sqrt(2+4*sqrt(2)))/((1/3)*sqrt(4+3*sqrt(2))*SA:V of Tetragonal Trapezohedron))^2)
Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((((3*Volume of Tetragonal Trapezohedron)/(sqrt(4+3*sqrt(2))))^(1/3))^2)

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