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Regular Tetrahedron Formula


In geometry, the other name for triangular pyramid is also taken as the tetrahedron that is composed of four triangular faces and six straight edges, and four vertex corners. This could also be defined as the simplest form of ordinary convex polyhedron having only fives faces less than five.

Area of One Face of Regular Tetrahedron Formula:

\[\large A=\frac{1}{4}\sqrt{3}a^{2}\]

Total Surface Area of Regular Tetrahedron Formula:

\[\large A=a^{2}\sqrt{3}\]

Slant Height of a Regular Tetrahedron Formula:

\[\large a\left(\frac{\sqrt{3}}{2}\right)\]

Altitude of a Regular Tetrahedron Formula:

\[\large h=\frac{a\sqrt{6}}{3}\]

Volume of a Regular Tetrahedron Formula

\[\large V=\frac{a^{3}\sqrt{2}}{12}\]

This is a 3-D shape that could also be defined as the special kind of pyramid with a flat polygon base and triangular faces that will connect the base with a common point. When we are talking about the tetrahedron, the base can be defined as the triangle so it is popular as the triangular pyramid.

This is possible folding the shape into a single sheet of paper. For every tetrahedron, there exists one sphere where all four vertices lie and another sphere is the tangent to tetrahedron’s faces. Now, it is further divided into two categories – regular tetrahedron and irregular tetrahedron. In the case of regular tetrahedron, the faces are of same size and shape, edges could be taken as of equal length.

Regular tetrahedron could not full the space but they have to arrange in such way that could make cubic honeycomb which is a tessellation. In most of the cases, regular tetrahedron are self-dual where dual is one more regular tetrahedron. Further, there could be some special cases too based on dimensions and other properties defined. One more case here is isosceles tetrahedron where all four faces would be congruent triangles.


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