A triangle is split in two. What is the area of the green quadrilateral in terms of lengths a and b?

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## Solution

The green area is (b^{2}-a^{2})/(4√3).

The trick is to note that the bottom angles add up to 60°. We can therefore fit together three copies of the quadrilateral as shown to form two concentric equilateral triangles of sides a and b.

Now it is simply a matter of subtracting the small triangle area a^{2}√3/4 from the large b^{2}√3/4 and dividing by 3.

## Poem

Below the tree line

Some disturbed vegetation

Of trees in a strange distribution

To measure direct interaction

With the rain and below average precipitation

It’s the highest elevation

Especially to avoid a gradual extinction

The tree line is the natural solution