Total Surface Area of Tetragonal Trapezohedron given Short Edge Calculator

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

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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 given Short Edge [TSA]

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Total Surface Area of Tetragonal Trapezohedron given Short Edge Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Short Edge of Tetragonal Trapezohedron - (Measured in Meter) - Short Edge of Tetragonal Trapezohedron is the length of any of the shorter edges of the Tetragonal Trapezohedron.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 2*sqrt(2+4*sqrt(2))*((l_e(Short)/(sqrt(sqrt(2)-1)))^2) --> 2*sqrt(2+4*sqrt(2))*((6/(sqrt(sqrt(2)-1)))^2)

Evaluating ... ...

TSA = 480.987036953673

STEP 3: Convert Result to Output's Unit

480.987036953673 Square Meter --> No Conversion Required

FINAL ANSWER

480.987036953673 ≈ 480.987 Square Meter <-- Total Surface Area of Tetragonal Trapezohedron

(Calculation completed in 00.004 seconds)

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< Total Surface Area of Tetragonal Trapezohedron Calculators

Total Surface Area of Tetragonal Trapezohedron given Long Edge

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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 given Short Edge Formula

LaTeX Go

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

Total Surface Area of Tetragonal Trapezohedron given Short Edge calculator uses Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))^2) to calculate the Total Surface Area of Tetragonal Trapezohedron, The Total Surface Area of Tetragonal Trapezohedron given Short Edge formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron, calculated using its short edge. Total Surface Area of Tetragonal Trapezohedron is denoted by TSA symbol.

How to calculate Total Surface Area of Tetragonal Trapezohedron given Short Edge using this online calculator? To use this online calculator for Total Surface Area of Tetragonal Trapezohedron given Short Edge, enter Short Edge of Tetragonal Trapezohedron (l_e(Short)) and hit the calculate button. Here is how the Total Surface Area of Tetragonal Trapezohedron given Short Edge calculation can be explained with given input values -> 480.987 = 2*sqrt(2+4*sqrt(2))*((6/(sqrt(sqrt(2)-1)))^2).

FAQ

What is Total Surface Area of Tetragonal Trapezohedron given Short Edge?

The Total Surface Area of Tetragonal Trapezohedron given Short Edge formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron, calculated using its short edge and is represented as TSA = 2*sqrt(2+4*sqrt(2))*((l_e(Short)/(sqrt(sqrt(2)-1)))^2) or Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))^2). Short Edge of Tetragonal Trapezohedron is the length of any of the shorter edges of the Tetragonal Trapezohedron.

How to calculate Total Surface Area of Tetragonal Trapezohedron given Short Edge?

The Total Surface Area of Tetragonal Trapezohedron given Short Edge formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron, calculated using its short edge is calculated using Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Short Edge of Tetragonal Trapezohedron/(sqrt(sqrt(2)-1)))^2). To calculate Total Surface Area of Tetragonal Trapezohedron given Short Edge, you need Short Edge of Tetragonal Trapezohedron (l_e(Short)). With our tool, you need to enter the respective value for Short Edge 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 Short Edge of Tetragonal Trapezohedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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 = 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)

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