At the base of the rectangular parallelepiped lies a rhombus, the dioganals of which are 16 and 12.

| February 13, 2021 | education

At the base of the rectangular parallelepiped lies a rhombus, the dioganals of which are 16 and 12. The section plane passing through two opposite edges of the upper and lower bases makes an angle of 45 degrees with the base. find the volume of the parallelepiped.

Since there is a rhombus at the base, the sides of the base are equal, AB = AD= BC = CD.

The diagonals of the rhombus intersect at right angles and at the point of intersection are divided in half, then the triangle AOD is rectangular, in which OA = AC / 2 = 16/2 = 8 cm, OD = ВD / 2 = 12/2 = 6 cm.Then, by the theorem Pythagoras AD ^ 2 = OA ^ 2 + OD ^ 2 = 64 + 36 = 100.

AD= СD = BC = AB = 10 cm.

Consider a right-angled triangle DСD1, in which the angle C = 450, then the angle D1 will be 450, and therefore the triangle is isosceles, СD = DD1 = 10 cm.

Let’s define the area of ​​a rhombus through its diagonals.

Sb = (AC * ВD) / 2 = 16 * 12/2 = 96 cm2.

Let’s define the volume of the parallelepiped.

V = Sbn * DD1 = 96 * 10 = 960 cm3.

Answer: The volume of the parallelepiped is 960 cm3.



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