In a regular hexagonal prism ABCDEFA1B1C1D1E1F1, all edges are 5 √5. Find the distance between points B1 and E.

univerkov | September 2, 2021 | education

At the base of the prism there is a regular hexagon, then the radius of the circle described around it is equal to the length of the edge of the hexagon. R = AB = 5 * √5 cm.

The large diagonal BE of the hexagon is the diameter of the circle circumscribed about the hexagon, then BE = 2 * R = 2 * 5 * √5 = 10 * √5 cm.

The triangle EBB1 is rectangular, with a right angle at point B, then, according to the Pythagorean theorem, EB1 ^ 2 = BE ^ 2 + BB1 ^ 2 = 500 + 125 = 625.

ВD = 25 cm.

Answer: the distance between points B1 and E is 25 cm.

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