# Given ABCDA1B1C1D1 is a straight line Prism, ABCD is a rhombus, the angle BCD

June 29, 2021 | education

| **Given ABCDA1B1C1D1 is a straight line Prism, ABCD is a rhombus, the angle BCD is 60 degrees, BB1 is 2, the angle B1B is 45 degrees, find the volume.**

Since the prism is straight, the triangle BB1D is rectangular, one of the angles is 45. Then the angle BB1D = 180 – 90 – 45 = 45, and then the triangle BB1D is isosceles and rectangular, which means that ВD = BB1 = 2 cm.

In a triangle ВСD ВС = DC as sides of a rhombus, and the angle ВСD = 60, then this triangle is equilateral and BC = DC = ВD = 2 cm.

Let’s calculate the area of the rhombus. Sromba = ВС * СD * Sin60 = 2 * 2 * √3 / 2 = 2 * √3 cm2.

Let us calculate the volume of the prism: Vrombus = Sbasn * BB1 = 2 * √3 * 2 = 4 * √3 cm2.

Answer: The volume of the prism is 4 * √3 cm2.

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