Three unit squares form the skeleton of a hexagon. What’s the area of the yellow rectangle?

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## Solution

The yellow rectangle is a square with area 3.

This figure is full of 30-60-90 triangles propagating from the equilateral triangle in the middle. Triangle FMC is one with hypothenuse 1 and middle side √3/2. From reflection symmetry in the vertical through M and C we deduce that the horizontal yellow rectangle side has length √3.

Also, triangle GLF is one, with middle side one and hypothenuse 2/√3 and short side 1/√3. From angle inspection we see that GLJ is isosceles, so we deduce LJ is also 1/√3. This makes the vertical side of the yellow rectangle √3 long as well.

## Poem

The lion the king of the jungle

The lion fights today in the sun

He is the boss the one

He likes the battles, and the fight

He is undefeated and good

The lion is hunting he knows he can

His story is known since centuries

He is a fighter without no mercy