A tetrahedron with given vertex coordinates. What is its volume?

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## Solution

The volume is 20.

The volume is symmetrical about the y=0 plane. Also AB is orthogonal to the y=0 plane. Thus we have two tetrahedra sharing a base triangle ECD and heights EA=EB=2. Filling the coordinates, the base triangle has surface 15, × 1/3 × height. 15×[1/3]×4 = 20.

## Poem

The axe is greedy

It bites the trees

It cuts the wood

And it frightens me !

The woodcutter works

With it all day long

From roots to canopy

Roaring with it’s saw

Or wields his axe fiercely

Life is not so easy

Sometimes much stress

But there is no mercy

He cuts and hacks the trees