3 Geometry Puzzles

Three Puzzles from Maurice the Cat.

First Puzzle: Two Brown upright poles of different heights are separated by W meters. The top of the each pole ia joined to the bottom of the opposite pole with an elastic cord The height where the cords meet is a distance we will call H above the ground.. If the right pole is moved to the position of the red pole – and the cords remaining attached – will the height where the cords cross remain the same, be higher, or be lower than H?

Second Two Puzzles In the left hand puzzle. A point inside a square is connected to its four vertices. What fraction of the square is shaded?. The point can be anywhere within the square. The answer is obviously a half but why? In the right hand puzzle A rectangle is constructed from the midpoints of the sides of a regular hexagon as shown. What fraction is shaded?


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