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Six congruent equilateral triangles placed outside 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 .

Bella

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