Face Area of Tetrahedron given Height Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Area of Tetrahedron = sqrt(3)/4*(sqrt(3/2)*Height of Tetrahedron)^2
AFace = sqrt(3)/4*(sqrt(3/2)*h)^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.
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.
STEP 1: Convert Input(s) to Base Unit
Height of Tetrahedron: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
AFace = sqrt(3)/4*(sqrt(3/2)*h)^2 --> sqrt(3)/4*(sqrt(3/2)*8)^2
Evaluating ... ...
AFace = 41.569219381653
STEP 3: Convert Result to Output's Unit
41.569219381653 Square Meter --> No Conversion Required
FINAL ANSWER
41.569219381653 41.56922 Square Meter <-- Face Area of Tetrahedron
(Calculation completed in 00.020 seconds)

Credits

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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 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

Face Area of Tetrahedron given Height Formula

Face Area of Tetrahedron = sqrt(3)/4*(sqrt(3/2)*Height of Tetrahedron)^2
AFace = sqrt(3)/4*(sqrt(3/2)*h)^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 given Height?

Face Area of Tetrahedron given Height calculator uses Face Area of Tetrahedron = sqrt(3)/4*(sqrt(3/2)*Height of Tetrahedron)^2 to calculate the Face Area of Tetrahedron, The Face Area of Tetrahedron given Height formula is defined as the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron, and calculated using the height of the Tetrahedron. Face Area of Tetrahedron is denoted by AFace symbol.

How to calculate Face Area of Tetrahedron given Height using this online calculator? To use this online calculator for Face Area of Tetrahedron given Height, enter Height of Tetrahedron (h) and hit the calculate button. Here is how the Face Area of Tetrahedron given Height calculation can be explained with given input values -> 41.56922 = sqrt(3)/4*(sqrt(3/2)*8)^2.

FAQ

What is Face Area of Tetrahedron given Height?
The Face Area of Tetrahedron given Height formula is defined as the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron, and calculated using the height of the Tetrahedron and is represented as AFace = sqrt(3)/4*(sqrt(3/2)*h)^2 or Face Area of Tetrahedron = sqrt(3)/4*(sqrt(3/2)*Height of Tetrahedron)^2. Height of Tetrahedron is the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex.
How to calculate Face Area of Tetrahedron given Height?
The Face Area of Tetrahedron given Height formula is defined as the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron, and calculated using the height of the Tetrahedron is calculated using Face Area of Tetrahedron = sqrt(3)/4*(sqrt(3/2)*Height of Tetrahedron)^2. To calculate Face Area of Tetrahedron given Height, you need Height of Tetrahedron (h). With our tool, you need to enter the respective value for Height 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 Height of Tetrahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Face Area of Tetrahedron = (sqrt(3))/4*Edge Length of Tetrahedron^2
  • 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)
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