The base of the straight prism is a rhombus with a side of 8 cm and an obtuse angle of 120 degrees.

| May 20, 2021 | education

The base of the straight prism is a rhombus with a side of 8 cm and an obtuse angle of 120 degrees. The smaller of the diagonal sections is square. Find the volume of the prism.

Since there is a rhombus at the base of the prism, its diagonals are the bisectors of the corners of the rhombus, then in the ABD triangle the angle ABD = ABC / 2 = 120/2 = 60.

Since AB = AD as the sides of the rhombus, the triangle ABD is equilateral, BD = AD = 8 cm.

BD is the smaller diagonal of the rhombus, then the section BB1D1D, by condition, is a square, then BB1 = DD1 = BD = 8 cm.

Determine the area of the base of the prism.

Sbn = AB * AD * Sin60 = 8 * 8 * √3 / 2 = 32 * √3 cm2.

Let’s define the volume of the prism.

V = Sbase * BB1 = 32 * √3 * 8 = 236 * √3 cm3.

Answer: The volume of the prism is 236 * √3 cm3.



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