Height of Elongated Pentagonal Pyramid given Total Surface Area Calculator

✖Total Surface Area of Elongated Pentagonal Pyramid is the total amount of two-dimensional space occupied by all the faces of the Elongated Pentagonal Pyramid.ⓘ Total Surface Area of Elongated Pentagonal Pyramid [TSA]

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✖Height of Elongated Pentagonal Pyramid is the vertical distance from the highest point to the lowest point of the Elongated Pentagonal Pyramid.ⓘ Height of Elongated Pentagonal Pyramid given Total Surface Area [h]

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Formula

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Height of Elongated Pentagonal Pyramid given Total Surface Area

Formula

`"h" = (sqrt((5-sqrt(5))/10)+1)*sqrt("TSA"/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5))`

Example

`"15.35527m"=(sqrt((5-sqrt(5))/10)+1)*sqrt("900m²"/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5))`

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Height of Elongated Pentagonal Pyramid given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*sqrt(Total Surface Area of Elongated Pentagonal Pyramid/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5))
h = (sqrt((5-sqrt(5))/10)+1)*sqrt(TSA/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5))
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

Height of Elongated Pentagonal Pyramid - (Measured in Meter) - Height of Elongated Pentagonal Pyramid is the vertical distance from the highest point to the lowest point of the Elongated Pentagonal Pyramid.
Total Surface Area of Elongated Pentagonal Pyramid - (Measured in Square Meter) - Total Surface Area of Elongated Pentagonal Pyramid is the total amount of two-dimensional space occupied by all the faces of the Elongated Pentagonal Pyramid.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Elongated Pentagonal Pyramid: 900 Square Meter --> 900 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (sqrt((5-sqrt(5))/10)+1)*sqrt(TSA/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5)) --> (sqrt((5-sqrt(5))/10)+1)*sqrt(900/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5))

Evaluating ... ...

h = 15.3552652037683

STEP 3: Convert Result to Output's Unit

15.3552652037683 Meter --> No Conversion Required

FINAL ANSWER

15.3552652037683 ≈ 15.35527 Meter <-- Height of Elongated Pentagonal Pyramid

(Calculation completed in 00.004 seconds)

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< 4 Height of Elongated Pentagonal Pyramid Calculators

Height of Elongated Pentagonal Pyramid given Surface to Volume Ratio

Go Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5)/(((5+sqrt(5))/24+(sqrt(25+(10*sqrt(5))))/4)*SA:V of Elongated Pentagonal Pyramid)

Height of Elongated Pentagonal Pyramid given Total Surface Area

Go Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*sqrt(Total Surface Area of Elongated Pentagonal Pyramid/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5))

Height of Elongated Pentagonal Pyramid given Volume

Go Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*(Volume of Elongated Pentagonal Pyramid/((5+sqrt(5))/24+(sqrt(25+(10*sqrt(5))))/4))^(1/3)

Height of Elongated Pentagonal Pyramid

Go Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*Edge Length of Elongated Pentagonal Pyramid

Height of Elongated Pentagonal Pyramid given Total Surface Area Formula

What is an Elongated Pentagonal Pyramid?

The Elongated Pentagonal Pyramid is a regular hexahedron with a matching pentagonal prism attached to one face, which is the Johnson solid generally denoted by J9. It consists of 11 faces which include 5 equilateral triangles as pyramid faces, 5 squares as side surfaces, and a regular pentagon as the base surface. Also, It has 20 edges and 11 vertices.

How to Calculate Height of Elongated Pentagonal Pyramid given Total Surface Area?

Height of Elongated Pentagonal Pyramid given Total Surface Area calculator uses Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*sqrt(Total Surface Area of Elongated Pentagonal Pyramid/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5)) to calculate the Height of Elongated Pentagonal Pyramid, The Height of Elongated Pentagonal Pyramid given Total Surface Area formula is defined as the vertical distance from the highest point to the lowest point of the Elongated Pentagonal Pyramid and is calculated using the total surface area of the Elongated Pentagonal Pyramid. Height of Elongated Pentagonal Pyramid is denoted by h symbol.

How to calculate Height of Elongated Pentagonal Pyramid given Total Surface Area using this online calculator? To use this online calculator for Height of Elongated Pentagonal Pyramid given Total Surface Area, enter Total Surface Area of Elongated Pentagonal Pyramid (TSA) and hit the calculate button. Here is how the Height of Elongated Pentagonal Pyramid given Total Surface Area calculation can be explained with given input values -> 15.35527 = (sqrt((5-sqrt(5))/10)+1)*sqrt(900/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5)).

FAQ

What is Height of Elongated Pentagonal Pyramid given Total Surface Area?

The Height of Elongated Pentagonal Pyramid given Total Surface Area formula is defined as the vertical distance from the highest point to the lowest point of the Elongated Pentagonal Pyramid and is calculated using the total surface area of the Elongated Pentagonal Pyramid and is represented as h = (sqrt((5-sqrt(5))/10)+1)*sqrt(TSA/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5)) or Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*sqrt(Total Surface Area of Elongated Pentagonal Pyramid/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5)). Total Surface Area of Elongated Pentagonal Pyramid is the total amount of two-dimensional space occupied by all the faces of the Elongated Pentagonal Pyramid.

How to calculate Height of Elongated Pentagonal Pyramid given Total Surface Area?

The Height of Elongated Pentagonal Pyramid given Total Surface Area formula is defined as the vertical distance from the highest point to the lowest point of the Elongated Pentagonal Pyramid and is calculated using the total surface area of the Elongated Pentagonal Pyramid is calculated using Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*sqrt(Total Surface Area of Elongated Pentagonal Pyramid/((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5)). To calculate Height of Elongated Pentagonal Pyramid given Total Surface Area, you need Total Surface Area of Elongated Pentagonal Pyramid (TSA). With our tool, you need to enter the respective value for Total Surface Area of Elongated Pentagonal 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 Height of Elongated Pentagonal Pyramid?

In this formula, Height of Elongated Pentagonal Pyramid uses Total Surface Area of Elongated Pentagonal Pyramid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*Edge Length of Elongated Pentagonal Pyramid
Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*(Volume of Elongated Pentagonal Pyramid/((5+sqrt(5))/24+(sqrt(25+(10*sqrt(5))))/4))^(1/3)
Height of Elongated Pentagonal Pyramid = (sqrt((5-sqrt(5))/10)+1)*((sqrt(25+(10*sqrt(5))))/4+(5*sqrt(3))/4+5)/(((5+sqrt(5))/24+(sqrt(25+(10*sqrt(5))))/4)*SA:V of Elongated Pentagonal Pyramid)

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