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

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.