Height of Tetrahedron given Face Area Calculator

✖Height of Tetrahedron is the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex.ⓘ Height of Tetrahedron given Face Area [h]

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Formula

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Height of Tetrahedron given Face Area

Formula

`"h" = sqrt((8*"A"_{"Face"})/(3*sqrt(3)))`

Example

`"8.323583m"=sqrt((8*"45m²")/(3*sqrt(3)))`

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Height of Tetrahedron given Face Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))
h = sqrt((8*A_Face)/(3*sqrt(3)))
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 Tetrahedron - (Measured in Meter) - Height of Tetrahedron is the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex.
Face Area of Tetrahedron - (Measured in Square Meter) - Face Area of Tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron.

STEP 1: Convert Input(s) to Base Unit

Face Area of Tetrahedron: 45 Square Meter --> 45 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt((8*A_Face)/(3*sqrt(3))) --> sqrt((8*45)/(3*sqrt(3)))

Evaluating ... ...

h = 8.32358290057563

STEP 3: Convert Result to Output's Unit

8.32358290057563 Meter --> No Conversion Required

FINAL ANSWER

8.32358290057563 ≈ 8.323583 Meter <-- Height of Tetrahedron

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

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< 8 Height of Tetrahedron Calculators

Height of Tetrahedron given Total Surface Area

Go Height of Tetrahedron = sqrt((2*Total Surface Area of Tetrahedron)/(3*sqrt(3)))

Height of Tetrahedron given Volume

Go Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)

Height of Tetrahedron given Face Area

Go Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))

Height of Tetrahedron given Midsphere Radius

Go Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron

Height of Tetrahedron

Go Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron

Height of Tetrahedron given Surface to Volume Ratio

Go Height of Tetrahedron = 12/Surface to Volume Ratio of Tetrahedron

Height of Tetrahedron given Circumsphere Radius

Go Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron

Height of Tetrahedron given Insphere Radius

Go Height of Tetrahedron = 4*Insphere Radius of Tetrahedron

< 4 Height of Tetrahedron Calculators

Height of Tetrahedron given Volume

Go Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)

Height of Tetrahedron given Face Area

Go Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))

Height of Tetrahedron

Go Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron

Height of Tetrahedron given Circumsphere Radius

Go Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron

Height of Tetrahedron given Face Area Formula

Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))
h = sqrt((8*A_Face)/(3*sqrt(3)))

What is a Tetrahedron?

A Tetrahedron is a symmetric and closed three dimensional shape with 4 identical equilateral triangular faces. It is a Platonic solid, which has 4 faces, 4 vertices and 6 edges. At each vertex, three equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Height of Tetrahedron given Face Area?

Height of Tetrahedron given Face Area calculator uses Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3))) to calculate the Height of Tetrahedron, The Height of Tetrahedron given Face Area formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the face area of the Tetrahedron. Height of Tetrahedron is denoted by h symbol.

How to calculate Height of Tetrahedron given Face Area using this online calculator? To use this online calculator for Height of Tetrahedron given Face Area, enter Face Area of Tetrahedron (A_Face) and hit the calculate button. Here is how the Height of Tetrahedron given Face Area calculation can be explained with given input values -> 8.323583 = sqrt((8*45)/(3*sqrt(3))).

FAQ

What is Height of Tetrahedron given Face Area?

The Height of Tetrahedron given Face Area formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the face area of the Tetrahedron and is represented as h = sqrt((8*A_Face)/(3*sqrt(3))) or Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3))). Face Area of Tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron.

How to calculate Height of Tetrahedron given Face Area?

The Height of Tetrahedron given Face Area formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the face area of the Tetrahedron is calculated using Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3))). To calculate Height of Tetrahedron given Face Area, you need Face Area of Tetrahedron (A_Face). With our tool, you need to enter the respective value for Face Area of Tetrahedron 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 Tetrahedron?

In this formula, Height of Tetrahedron uses Face Area of Tetrahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -

Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron
Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron
Height of Tetrahedron = 4*Insphere Radius of Tetrahedron
Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron
Height of Tetrahedron = 12/Surface to Volume Ratio of Tetrahedron
Height of Tetrahedron = sqrt((2*Total Surface Area of Tetrahedron)/(3*sqrt(3)))
Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)
Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron
Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron
Height of Tetrahedron = sqrt(2/3)*(6*sqrt(2)*Volume of Tetrahedron)^(1/3)

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