Given a rectangular parallelepiped, which is based on a rhombus with a smaller diagonal of 6 cm

univerkov | September 17, 2021 | education

Given a rectangular parallelepiped, which is based on a rhombus with a smaller diagonal of 6 cm and an angle of 60 degrees, the side edge is half the edge of the base. Find V -?

Since there is a rhombus at the base of the parallelepiped, then AB = BC = CD = AD.

Triangle ABD is isosceles, and since its acute angle is 60, triangle ABD is isosceles, AB = AD = BD = 6 cm.

Determine the area of the base of the parallelepiped.

Sbn = AB * AD * Sin60 = 6 * 6 * √3 / 2 = 18 * √3 cm2.

By the condition AA1 = AB / 2 = 6/2 = 3 cm.

Since the parallelepiped is straight, then V = Sсн * АА1 = 18 * √3 * 3 = 54 * √3cm3.

Answer: The volume is 54 * √3cm3.

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