Total Surface Area of Gyroelongated Square Pyramid given Height Calculator

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

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

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Total Surface Area of Gyroelongated Square Pyramid given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*(Height of Gyroelongated Square Pyramid/(sqrt(1-1/(2+sqrt(2)))+1/sqrt(2)))^2
SA_Total = (1+(3*sqrt(3)))*(h/(sqrt(1-1/(2+sqrt(2)))+1/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 Pyramid - (Measured in Square Meter) - TSA of Gyroelongated Square Pyramid is the total amount of two-dimensional space occupied by all the faces of the Gyroelongated Square Pyramid.
Height of Gyroelongated Square Pyramid - (Measured in Meter) - Height of Gyroelongated Square Pyramid is the vertical distance from the highest point to the lowest point of the Gyroelongated Square Pyramid.

STEP 1: Convert Input(s) to Base Unit

Height of Gyroelongated Square Pyramid: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

SA_Total = (1+(3*sqrt(3)))*(h/(sqrt(1-1/(2+sqrt(2)))+1/sqrt(2)))^2 --> (1+(3*sqrt(3)))*(15/(sqrt(1-1/(2+sqrt(2)))+1/sqrt(2)))^2

Evaluating ... ...

SA_Total = 581.782836266155

STEP 3: Convert Result to Output's Unit

581.782836266155 Square Meter --> No Conversion Required

FINAL ANSWER

581.782836266155 ≈ 581.7828 Square Meter <-- TSA of Gyroelongated Square Pyramid

(Calculation completed in 00.006 seconds)

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< Surface Area of Gyroelongated Square Pyramid Calculators

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

LaTeX Go TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*SA:V of Gyroelongated Square Pyramid))^2

Total Surface Area of Gyroelongated Square Pyramid given Volume

LaTeX Go TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((3*Volume of Gyroelongated Square Pyramid)/(sqrt(4+(3*sqrt(2)))+1/sqrt(2)))^(2/3)

Total Surface Area of Gyroelongated Square Pyramid given Height

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

Total Surface Area of Gyroelongated Square Pyramid

LaTeX Go TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*Edge Length of Gyroelongated Square Pyramid^2

Total Surface Area of Gyroelongated Square Pyramid given Height Formula

LaTeX Go

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

What is a Gyroelongated Square Pyramid?

The Gyroelongated Square Pyramid is a regular johnson square pyramid with a matching antiprism attached to the base, which is the Johnson solid generally denoted by J10. It consists of 13 faces which include 12 equilateral triangles as side surfaces, and a square as the base surface. Also, It has 20 edges and 9 vertices.

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

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

How to calculate Total Surface Area of Gyroelongated Square Pyramid given Height using this online calculator? To use this online calculator for Total Surface Area of Gyroelongated Square Pyramid given Height, enter Height of Gyroelongated Square Pyramid (h) and hit the calculate button. Here is how the Total Surface Area of Gyroelongated Square Pyramid given Height calculation can be explained with given input values -> 581.7828 = (1+(3*sqrt(3)))*(15/(sqrt(1-1/(2+sqrt(2)))+1/sqrt(2)))^2.

FAQ

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

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

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

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

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

TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*Edge Length of Gyroelongated Square Pyramid^2
TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((3*Volume of Gyroelongated Square Pyramid)/(sqrt(4+(3*sqrt(2)))+1/sqrt(2)))^(2/3)
TSA of Gyroelongated Square Pyramid = (1+(3*sqrt(3)))*((1+(3*sqrt(3)))/(((sqrt(4+(3*sqrt(2)))+1/sqrt(2))/3)*SA:V of Gyroelongated Square Pyramid))^2

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