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
