In a regular hexagonal pyramid, the side of its base is 2, volume 6. Match the height.

univerkov | March 4, 2021 | education

Since a regular hexagon lies at the base of the pyramid, its large diagonals divide it into six equal-sized, equilateral triangles with sides of 2 cm. Let us determine the area of one such triangle.

Saov = a ^ 2 * √3 / 4, where a is the side of a regular triangle.

Saov = 4 * √3 / 4 = √3 cm2.

Then the area of the base of the pyramid is equal to: Sbn = 6 * Saov = 6 * √3 cm2.

The volume of the pyramid is equal to: V = Sosn * SO / 3.

SO = 3 * V / Sb = 3 * 6 / (6 * √3) = 3 / √3 = √3 cm.

Answer: The height of the pyramid is √3 cm.

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