Complete Explanation for Volume of a Tetrahedron

In this video we derive the volume of a tetrahedron with the help of Euclid.

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[handle--]

I like how consistent he is from 10 years

[charlesbromberick]

Taking the integral of various triangular slices is fun, too.

[HaileISela]

now, another way of going about this is to say the area of the base is one ETU (equilateral triangle unit), and its volume is one quantumvolume. this way the eighteyes ("octahedron") has a surface area of eight ETU and a quantumvolume of four, the dozeneighteyes ("icosahedron") has a dozeneight ETU and a qv of one and a half dozen plus a golden rest (one can find the precise value/formula on the wikipedia entry on "Synergetics (Fuller)"), while the omni-triangulated 'cube' with the face diagonal being one (same as the edge of the ETU) and therefore edges of +-sqrt1/2 having a quantumvolume of three.

[DeuryMota-go]

Hello thanks thank You for your information for your explanation

[sleuth]

How is AD = side of the equalateral triangle ?

[jmarchito]

What if the sides of ABC are scalene triangle?

[BeeeeepBoop]

What if it's an isosceles tetrahedron?

[Science__Politics]

What if I want to know the volume of a regular tetrahedron based on its height?

[sodahead]

You can get the height of your tetrahedron and then do the integral of a cross section from 0 to h.

[Science__Politics]

I just googled this by chance this happen to have just come out within the same month