Six congruent equilateral triangles placed inside a regular hexagon. What fraction is coloured?

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## Solution

The coloured fraction is 4/7.

Set the inner hexagon side to 1. The triangles then have side 2, so their total area 6√3. Now from the diagram above you can deduce that the side of the outer regular hexagon is √7. It’s area is 21√3/2. The required fraction follows.

## Poem

Congruent by Euclides

Means the same in geometry

So they are similar

Let’s think about a congruent

Humanity

What would that be?

Are we proportional?

Are our structures good for relationship?

Can we substitute one another?

In the Mathematical Poetry

The result was

Four different poems

Logically equivalent

Each poem says the same thing

With a different flavor

We are congruent if we are mutual

In our thoughts and reactions

But we are different .