A square whose sides each measure ten centimeters can completely fit inside of a regular hexagon whose sides each measure ten centimeters.
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True
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False
To solve this question, the user needs to know the properties of both squares and hexagons.
A square is a four-sided polygon with all sides of equal length and all interior angles equal to 90 degrees. A regular hexagon is a six-sided polygon with all sides of equal length and all interior angles equal to 120 degrees.
It is known that a square can fit inside a circle whose diameter is equal to the length of the square's sides. The circle circumscribing a regular hexagon has a diameter equal to the length of the hexagon's sides.
Therefore, if the square's sides each measure ten centimeters, then the diameter of the circumscribing circle is also ten centimeters. Since the square can fit inside this circle, it can also fit inside the regular hexagon whose sides each measure ten centimeters.
Hence, the correct option is:
The Answer is: A. True
A regular hexagon with side 10 cm has a flat-to-flat width of 10√3 ≈ 17.3 cm, which comfortably exceeds the roughly 14.1 cm diagonal of a 10 cm square. Since the square's largest dimension fits well within the hexagon's narrowest internal width, the square can be positioned to fit entirely inside, making the statement true.