In a regular hexagonal prism ABCDEFA1B1C1D1E1F1, all edges are 3√5. Find the distance between points B and E1.

univerkov | August 16, 2021 | education

Since a regular hexagon lies at the base of the prism, the radius of the circumscribed circle 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 = 6 * √5 cm.

In a right-angled triangle ADD1, according to the Pythagorean theorem, we determine the length of the hypotenuse AD1.

BE1 ^ 2 = BE ^ 2 + EE1 ^ 2 = (6 * √5) ^ 2 + (3 * √5) ^ 2 = 180 + 45 = 225.

AD1 = 15 cm.

Answer: The distance from point B to point E1 is 15 cm.

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