At the base of the straight prism is a rhombus; the diagonals of the prism make angles of 30 degrees and 60 degrees with the base plane; the height of the prism is 6cm. Find its volume.
In a right-angled triangle ВDD1, by condition, the angle DBD1 = 60, then tg60 = DD1 / ВD, then ВD = DD1 / tg60 = 6 / √3 = 6 * √3 / √3 * √3 = 2 * √3 cm.
In a right-angled triangle AA1C, we determine the length of the leg AC.
Tg30 = АА1 / АС, then FC = AA1 / tg30 = 6 / (√3 / 3) = 18 / √3 = 6 * √3 cm.
Determine the area of the base of the prism.
Sbn = АС * ВD / 2 = 2 * √3 * 6 * √3 / 2 = 18 cm2.
Let’s define the volume of the prism.
Vpr = Sbn * AA1 = 18 * 6 = 108 cm3.
Answer: The volume of the prism is 108 cm3.
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