Total Surface Area of Tetragonal Trapezohedron given Height Calculator

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

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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 Height [TSA]

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Total Surface Area of Tetragonal Trapezohedron given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^2)
TSA = 2*sqrt(2+4*sqrt(2))*((h/(sqrt((1/2)*(4+3*sqrt(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 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.
Height of Tetragonal Trapezohedron - (Measured in Meter) - Height of Tetragonal Trapezohedron is the distance between the two peak vertices where the long edges of Tetragonal Trapezohedron join.

STEP 1: Convert Input(s) to Base Unit

Height of Tetragonal Trapezohedron: 20 Meter --> 20 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 2*sqrt(2+4*sqrt(2))*((h/(sqrt((1/2)*(4+3*sqrt(2)))))^2) --> 2*sqrt(2+4*sqrt(2))*((20/(sqrt((1/2)*(4+3*sqrt(2)))))^2)

Evaluating ... ...

TSA = 537.129251533291

STEP 3: Convert Result to Output's Unit

537.129251533291 Square Meter --> No Conversion Required

FINAL ANSWER

537.129251533291 ≈ 537.1293 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 Height Formula

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)
TSA = 2*sqrt(2+4*sqrt(2))*((h/(sqrt((1/2)*(4+3*sqrt(2)))))^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 Height?

Total Surface Area of Tetragonal Trapezohedron given Height calculator uses Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^2) to calculate the Total Surface Area of Tetragonal Trapezohedron, The Total Surface Area of Tetragonal Trapezohedron given Height formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron, calculated using its height. Total Surface Area of Tetragonal Trapezohedron is denoted by TSA symbol.

How to calculate Total Surface Area of Tetragonal Trapezohedron given Height using this online calculator? To use this online calculator for Total Surface Area of Tetragonal Trapezohedron given Height, enter Height of Tetragonal Trapezohedron (h) and hit the calculate button. Here is how the Total Surface Area of Tetragonal Trapezohedron given Height calculation can be explained with given input values -> 537.1293 = 2*sqrt(2+4*sqrt(2))*((20/(sqrt((1/2)*(4+3*sqrt(2)))))^2).

FAQ

What is Total Surface Area of Tetragonal Trapezohedron given Height?

The Total Surface Area of Tetragonal Trapezohedron given Height formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron, calculated using its height and is represented as TSA = 2*sqrt(2+4*sqrt(2))*((h/(sqrt((1/2)*(4+3*sqrt(2)))))^2) or Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^2). Height of Tetragonal Trapezohedron is the distance between the two peak vertices where the long edges of Tetragonal Trapezohedron join.

How to calculate Total Surface Area of Tetragonal Trapezohedron given Height?

The Total Surface Area of Tetragonal Trapezohedron given Height formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Tetragonal Trapezohedron, calculated using its height is calculated using Total Surface Area of Tetragonal Trapezohedron = 2*sqrt(2+4*sqrt(2))*((Height of Tetragonal Trapezohedron/(sqrt((1/2)*(4+3*sqrt(2)))))^2). To calculate Total Surface Area of Tetragonal Trapezohedron given Height, you need Height of Tetragonal Trapezohedron (h). With our tool, you need to enter the respective value for Height 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 Height 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))*(((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)

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