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What I have been told: There's a irregular tetrahedron(pyramid with a base of a triangle), I know that three edges that form the tip are of length 2(a),3(b) and 4(c) and all edges at the one tip, where I have been given all the lengths are crosswise, so ∠ab = 90 ; ∠bc = 90 and ∠ac = 90.

What I know how to do: From here I can easily calculate all six edges of the tetrahedron and also the surface are.

What I am asked to do:find the volume.

Any tips and ideas would be awesome

Apologies for the poor english and if I wasn't clear, please tell me.

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2 Answers

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Hint: If I read you correctly $c$ is already perpendicular on the plane generated by $a$ and $b$. No need to hunt for height. The base opposing this height is a solvable right triangle.

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If there are 3 edges length a,b and c perpendicular to each other, then

Volume = $1/3* c * a b/2 = a b c/ 6$

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