Face Area of Tetrahedron Calculator

✖Edge Length of Tetrahedron is the length of any of edges of the Tetrahedron or the distance between any pair of adjacent vertices of the Tetrahedron.ⓘ Edge Length of Tetrahedron [l_e]

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✖Face Area of Tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron.ⓘ Face Area of Tetrahedron [A_Face]

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Formula

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Face Area of Tetrahedron

Formula

`"A"_{"Face"} = (sqrt(3))/4*"l"_{"e"}^2`

Example

`"43.30127m²"=(sqrt(3))/4*("10m")^2`

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Face Area of Tetrahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Face Area of Tetrahedron = (sqrt(3))/4*Edge Length of Tetrahedron^2
A_Face = (sqrt(3))/4*l_e^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

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.
Edge Length of Tetrahedron - (Measured in Meter) - Edge Length of Tetrahedron is the length of any of edges of the Tetrahedron or the distance between any pair of adjacent vertices of the Tetrahedron.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Tetrahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Face = (sqrt(3))/4*l_e^2 --> (sqrt(3))/4*10^2

Evaluating ... ...

A_Face = 43.3012701892219

STEP 3: Convert Result to Output's Unit

43.3012701892219 Square Meter --> No Conversion Required

FINAL ANSWER

43.3012701892219 ≈ 43.30127 Square Meter <-- Face Area of Tetrahedron

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Verified by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 8 Face Area of Tetrahedron Calculators

Face Area of Tetrahedron given Circumsphere Radius

Go Face Area of Tetrahedron = (sqrt(3))/4*((2*sqrt(2)*Circumsphere Radius of Tetrahedron)/sqrt(3))^2

Face Area of Tetrahedron given Surface to Volume Ratio

Go Face Area of Tetrahedron = sqrt(3)/4*((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^2

Face Area of Tetrahedron given Midsphere Radius

Go Face Area of Tetrahedron = (sqrt(3))/4*(2*sqrt(2)*Midsphere Radius of Tetrahedron)^2

Face Area of Tetrahedron given Volume

Go Face Area of Tetrahedron = sqrt(3)/4*(6*sqrt(2)*Volume of Tetrahedron)^(2/3)

Face Area of Tetrahedron given Height

Go Face Area of Tetrahedron = sqrt(3)/4*(sqrt(3/2)*Height of Tetrahedron)^2

Face Area of Tetrahedron given Insphere Radius

Go Face Area of Tetrahedron = 6*sqrt(3)*Insphere Radius of Tetrahedron^2

Face Area of Tetrahedron

Go Face Area of Tetrahedron = (sqrt(3))/4*Edge Length of Tetrahedron^2

Face Area of Tetrahedron given Total Surface Area

Go Face Area of Tetrahedron = Total Surface Area of Tetrahedron/4

< 6 Surface Area of Tetrahedron Calculators

Total Surface Area of Tetrahedron given Circumsphere Radius

Go Total Surface Area of Tetrahedron = sqrt(3)*((2*sqrt(2)*Circumsphere Radius of Tetrahedron)/sqrt(3))^2

Total Surface Area of Tetrahedron given Volume

Go Total Surface Area of Tetrahedron = sqrt(3)*((12*Volume of Tetrahedron)/sqrt(2))^(2/3)

Total Surface Area of Tetrahedron given Height

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

Total Surface Area of Tetrahedron

Go Total Surface Area of Tetrahedron = sqrt(3)*Edge Length of Tetrahedron^2

Face Area of Tetrahedron given Insphere Radius

Go Face Area of Tetrahedron = 6*sqrt(3)*Insphere Radius of Tetrahedron^2

Face Area of Tetrahedron

Go Face Area of Tetrahedron = (sqrt(3))/4*Edge Length of Tetrahedron^2

Face Area of Tetrahedron Formula

Face Area of Tetrahedron = (sqrt(3))/4*Edge Length of Tetrahedron^2
A_Face = (sqrt(3))/4*l_e^2

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 Face Area of Tetrahedron?

Face Area of Tetrahedron calculator uses Face Area of Tetrahedron = (sqrt(3))/4*Edge Length of Tetrahedron^2 to calculate the Face Area of Tetrahedron, Face Area of Tetrahedron formula is defined as the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron. Face Area of Tetrahedron is denoted by A_Face symbol.

How to calculate Face Area of Tetrahedron using this online calculator? To use this online calculator for Face Area of Tetrahedron, enter Edge Length of Tetrahedron (l_e) and hit the calculate button. Here is how the Face Area of Tetrahedron calculation can be explained with given input values -> 43.30127 = (sqrt(3))/4*10^2.

FAQ

What is Face Area of Tetrahedron?

Face Area of Tetrahedron formula is defined as the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron and is represented as A_Face = (sqrt(3))/4*l_e^2 or Face Area of Tetrahedron = (sqrt(3))/4*Edge Length of Tetrahedron^2. Edge Length of Tetrahedron is the length of any of edges of the Tetrahedron or the distance between any pair of adjacent vertices of the Tetrahedron.

How to calculate Face Area of Tetrahedron?

Face Area of Tetrahedron formula is defined as the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron is calculated using Face Area of Tetrahedron = (sqrt(3))/4*Edge Length of Tetrahedron^2. To calculate Face Area of Tetrahedron, you need Edge Length of Tetrahedron (l_e). With our tool, you need to enter the respective value for Edge Length 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 Face Area of Tetrahedron?

In this formula, Face Area of Tetrahedron uses Edge Length of Tetrahedron. We can use 8 other way(s) to calculate the same, which is/are as follows -

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

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