In a regular hexagonal prism ABCDEFA1B1C1D1E1F1, all edges of which are equal to √5, find the distance between points B and E1.
Since a regular hexagon lies at the base of the prism, the radius of the circle described around it is equal to the length of the side of this hexagon, and its large diagonals are the diameters of this circle, then BE = 2 * R = 2 * AB = D = 2 * √5 cm.
In a right-angled triangle BEE1, by the Pythagorean theorem, we determine the length of the hypotenuse BE1.
BE1 ^ 2 = BE ^ 2 + EE1 ^ 2 = (2 * √5) ^ 2 + (√5) ^ 2 = 20 + 5 = 25.
BE1 = 5 cm.
Answer: The distance from point B to point E1 is 5 cm.
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