Total Surface Area of Pentagonal Trapezohedron Calculator

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

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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 [TSA]

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Total Surface Area of Pentagonal Trapezohedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*(Antiprism Edge Length of Pentagonal Trapezohedron^2)
TSA = (sqrt((25/2)*(5+sqrt(5))))*(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 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.
Antiprism Edge Length of Pentagonal Trapezohedron - (Measured in Meter) - Antiprism Edge Length of Pentagonal Trapezohedron is the distance between any pair of adjacent vertices of the antiprism which corresponds to the Pentagonal Trapezohedron.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (sqrt((25/2)*(5+sqrt(5))))*(l_e(Antiprism)^2) --> (sqrt((25/2)*(5+sqrt(5))))*(10^2)

Evaluating ... ...

TSA = 951.056516295154

STEP 3: Convert Result to Output's Unit

951.056516295154 Square Meter --> No Conversion Required

FINAL ANSWER

951.056516295154 ≈ 951.0565 Square Meter <-- Total Surface Area of Pentagonal Trapezohedron

(Calculation completed in 00.004 seconds)

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< Surface Area of Pentagonal Trapezohedron Calculators

Total Surface Area of Pentagonal Trapezohedron given Height

LaTeX 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 Short Edge

LaTeX 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

LaTeX 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

LaTeX 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 Formula

LaTeX Go

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

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

How to calculate Total Surface Area of Pentagonal Trapezohedron using this online calculator? To use this online calculator for Total Surface Area of Pentagonal Trapezohedron, enter Antiprism Edge Length of Pentagonal Trapezohedron (l_e(Antiprism)) and hit the calculate button. Here is how the Total Surface Area of Pentagonal Trapezohedron calculation can be explained with given input values -> 951.0565 = (sqrt((25/2)*(5+sqrt(5))))*(10^2).

FAQ

What is Total Surface Area of Pentagonal Trapezohedron?

The Total Surface Area of Pentagonal Trapezohedron formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Pentagonal Trapezohedron and is represented as TSA = (sqrt((25/2)*(5+sqrt(5))))*(l_e(Antiprism)^2) or Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*(Antiprism Edge Length of Pentagonal Trapezohedron^2). Antiprism Edge Length of Pentagonal Trapezohedron is the distance between any pair of adjacent vertices of the antiprism which corresponds to the Pentagonal Trapezohedron.

How to calculate Total Surface Area of Pentagonal Trapezohedron?

The Total Surface Area of Pentagonal Trapezohedron formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Pentagonal Trapezohedron is calculated using Total Surface Area of Pentagonal Trapezohedron = (sqrt((25/2)*(5+sqrt(5))))*(Antiprism Edge Length of Pentagonal Trapezohedron^2). To calculate Total Surface Area of Pentagonal Trapezohedron, you need Antiprism Edge Length of Pentagonal Trapezohedron (l_e(Antiprism)). With our tool, you need to enter the respective value for Antiprism Edge Length 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 Antiprism Edge Length of Pentagonal Trapezohedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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))))*((Long 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)

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