A rectangular parallelepiped is given, the lengths of the sides are 3 and 4 cm, the angle between

| August 16, 2021 | education

A rectangular parallelepiped is given, the lengths of the sides are 3 and 4 cm, the angle between them is 60. Sside = 15√3. Find the volume.

As far as it is clear from the condition, at the base there is a parallelogram with sides of 3 and 4 cm, and an angle between them of 60 degrees. We immediately determine the area of the base S1 = 3 * 4 * sin (60) = 12 * √ (3) / 2 = 6 * √ ( 3).
The area of the lateral surface of the parallelepiped Sside is (base perimeter) * height = 15 * √ (3). From here we determine the height of the parallelepiped by determining its perimeter 2 * (3 + 4) = 14.
Height = h = Sside / 14 = 15 * √ (3) / 14 = 15 * √ (3) / 14.
Now let’s determine the volume of the parallelepiped V.
V = S1 * h = 6 * √ (3) * 15 * √ (3) / 14 = 18 * 15/14 = 135/7.



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