Stars inside Hexagon
Geometry
Level
2
A series of stars are drawn repeatedly inside the outermost hexagon with unit area, as shown.
If this process continues indefinitely towards the center, what is the total area shaded red?
The answer is 0.5.
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1 solution
By looking at the picture below, we can see that 6 red triangles and 6 white triangles are repeated inside each Hexagon.
And we can see also from the rectangle that the red triangle are is equal to the white triangle area.
R e d f r o m t o t a l a r e a = 1 + 1 1 = 0 . 5