Total Surface Area of Gyroelongated Square Dipyramid given Height Calculator

✖Height of Gyroelongated Square Dipyramid is the vertical distance from the highest point to the lowest point of the Gyroelongated Square Dipyramid.ⓘ Height of Gyroelongated Square Dipyramid [h]

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✖TSA of Gyroelongated Square Dipyramid is the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Square Dipyramid.ⓘ Total Surface Area of Gyroelongated Square Dipyramid given Height [SA_Total]

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Formula

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Total Surface Area of Gyroelongated Square Dipyramid given Height

Formula

`"SA"_{"Total"} = 4*sqrt(3)*("h"/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2`

Example

`"659.372m²"=4*sqrt(3)*("22m"/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2`

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Total Surface Area of Gyroelongated Square Dipyramid given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*(Height of Gyroelongated Square Dipyramid/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2
SA_Total = 4*sqrt(3)*(h/(sqrt(1-1/(2+sqrt(2)))+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

TSA of Gyroelongated Square Dipyramid - (Measured in Square Meter) - TSA of Gyroelongated Square Dipyramid is the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Square Dipyramid.
Height of Gyroelongated Square Dipyramid - (Measured in Meter) - Height of Gyroelongated Square Dipyramid is the vertical distance from the highest point to the lowest point of the Gyroelongated Square Dipyramid.

STEP 1: Convert Input(s) to Base Unit

Height of Gyroelongated Square Dipyramid: 22 Meter --> 22 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

SA_Total = 4*sqrt(3)*(h/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2 --> 4*sqrt(3)*(22/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2

Evaluating ... ...

SA_Total = 659.372039968699

STEP 3: Convert Result to Output's Unit

659.372039968699 Square Meter --> No Conversion Required

FINAL ANSWER

659.372039968699 ≈ 659.372 Square Meter <-- TSA of Gyroelongated Square Dipyramid

(Calculation completed in 00.004 seconds)

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< 4 Surface Area of Gyroelongated Square Dipyramid Calculators

Total Surface Area of Gyroelongated Square Dipyramid given Surface to Volume Ratio

Go TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*((12*sqrt(3))/((sqrt(2)+sqrt(4+(3*sqrt(2))))*SA:V of Gyroelongated Square Dipyramid))^2

Total Surface Area of Gyroelongated Square Dipyramid given Volume

Go TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*((3*Volume of Gyroelongated Square Dipyramid)/(sqrt(2)+sqrt(4+(3*sqrt(2)))))^(2/3)

Total Surface Area of Gyroelongated Square Dipyramid given Height

Go TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*(Height of Gyroelongated Square Dipyramid/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2

Total Surface Area of Gyroelongated Square Dipyramid

Go TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*Edge Length of Gyroelongated Square Dipyramid^2

Total Surface Area of Gyroelongated Square Dipyramid given Height Formula

TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*(Height of Gyroelongated Square Dipyramid/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2
SA_Total = 4*sqrt(3)*(h/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2

What is a Gyroelongated Square Dipyramid?

The Gyroelongated Square Dipyramid is a regular johnson square pyramid with a matching antiprism attached to the base and another regular square pyramid to the other side, which is the Johnson solid generally denoted by J17. It consists of 16 equilateral triangular faces. Also, It has 24 edges and 10 vertices.

How to Calculate Total Surface Area of Gyroelongated Square Dipyramid given Height?

Total Surface Area of Gyroelongated Square Dipyramid given Height calculator uses TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*(Height of Gyroelongated Square Dipyramid/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2 to calculate the TSA of Gyroelongated Square Dipyramid, The Total Surface Area of Gyroelongated Square Dipyramid given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Square Dipyramid and is calculated using the height of the Gyroelongated Square Dipyramid. TSA of Gyroelongated Square Dipyramid is denoted by SA_Total symbol.

How to calculate Total Surface Area of Gyroelongated Square Dipyramid given Height using this online calculator? To use this online calculator for Total Surface Area of Gyroelongated Square Dipyramid given Height, enter Height of Gyroelongated Square Dipyramid (h) and hit the calculate button. Here is how the Total Surface Area of Gyroelongated Square Dipyramid given Height calculation can be explained with given input values -> 659.372 = 4*sqrt(3)*(22/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2.

FAQ

What is Total Surface Area of Gyroelongated Square Dipyramid given Height?

The Total Surface Area of Gyroelongated Square Dipyramid given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Square Dipyramid and is calculated using the height of the Gyroelongated Square Dipyramid and is represented as SA_Total = 4*sqrt(3)*(h/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2 or TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*(Height of Gyroelongated Square Dipyramid/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2. Height of Gyroelongated Square Dipyramid is the vertical distance from the highest point to the lowest point of the Gyroelongated Square Dipyramid.

How to calculate Total Surface Area of Gyroelongated Square Dipyramid given Height?

The Total Surface Area of Gyroelongated Square Dipyramid given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Square Dipyramid and is calculated using the height of the Gyroelongated Square Dipyramid is calculated using TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*(Height of Gyroelongated Square Dipyramid/(sqrt(1-1/(2+sqrt(2)))+sqrt(2)))^2. To calculate Total Surface Area of Gyroelongated Square Dipyramid given Height, you need Height of Gyroelongated Square Dipyramid (h). With our tool, you need to enter the respective value for Height of Gyroelongated Square Dipyramid 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 TSA of Gyroelongated Square Dipyramid?

In this formula, TSA of Gyroelongated Square Dipyramid uses Height of Gyroelongated Square Dipyramid. We can use 3 other way(s) to calculate the same, which is/are as follows -

TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*Edge Length of Gyroelongated Square Dipyramid^2
TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*((3*Volume of Gyroelongated Square Dipyramid)/(sqrt(2)+sqrt(4+(3*sqrt(2)))))^(2/3)
TSA of Gyroelongated Square Dipyramid = 4*sqrt(3)*((12*sqrt(3))/((sqrt(2)+sqrt(4+(3*sqrt(2))))*SA:V of Gyroelongated Square Dipyramid))^2

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