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Face Area of Tetrahedron given Insphere Radius Calculator

Formula

The formula to calculate the Face Area of Tetrahedron (AFace) is:

$A_{Face} = 6 \cdot \sqrt{3} \cdot ri^2$

Where:

$A_{Face}$ is the Face Area of Tetrahedron (measured in square meters).
$ri$ is the Insphere Radius of Tetrahedron (measured in meters).

Definition

Face Area of Tetrahedron is the quantity of plane enclosed by any equilateral triangular face of the Tetrahedron.

Insphere Radius of Tetrahedron is the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touch the sphere.

How to calculate Face Area of Tetrahedron

Let's assume the following value:

Insphere Radius of Tetrahedron (ri) = 2 meters

Using the formula:

$A_{Face} = 6 \cdot \sqrt{3} \cdot 2^2$

Evaluating:

$A_{Face} \approx 41.5692 \, \text{square meters}$

The Face Area of Tetrahedron is approximately 41.5692 square meters.

Conversion Chart

Insphere Radius (ri) (meters)	Face Area (AFace) (square meters)
1.5	23.3827
2	41.5692
2.5	64.9519