At the base of a straight parallelepiped lies a rhombus with a side of 4 and an acute angle of 30 degrees.

| September 9, 2021 | education

At the base of a straight parallelepiped lies a rhombus with a side of 4 and an acute angle of 30 degrees. Find the volume of a parallelepiped if the diagonal of its side face is 5.

As you know, the volume of a parallelepiped is equal to the product of the area of ​​the base and the height. Let’s find the area of ​​the base.

The height of a rhombus is equal to the product of its side and the sine of an acute angle. In this case, the height will be equal to:

4 * 1/2 = 2.

This means that the base area of ​​this parallelepiped is:

S = 4 * 2 = 8.

The side face of this parallelepiped is a rectangle with a length of 4 and a diagonal of 5. This means the second side of the side face, that is, the height of the parallelepiped will be:

х² = 5² – 4²,

x² = 25 – 16,

x² = 9,

x = 3.

Thus, the volume of the parallelepiped is:

V = 8 * 3 = 24.



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