At the base of the inclined prism, a rhombus with a diagonal of 24 cm and a side of 37 cm. Determine the volume

| August 11, 2021 | education

At the base of the inclined prism, a rhombus with a diagonal of 24 cm and a side of 37 cm. Determine the volume of the prism if the perpendicular section passing through the large diagonal of the rhombus has an area of 1400 cm ^ 2.

Since the diagonals of the rhombus intersect at right angles, the triangle AOB is rectangular, in which the hypotenuse AB = 37 cm, the leg OB = BD / 2 = 24/2 = 12 cm.

Then AO ^ 2 = AB ^ 2 – OB ^ 2 = 37 ^ 2 – 12 ^ 2 = 1369 – 144 = 1225.

AO = 35 cm, then AC = 2 * 35 = 70 cm.

By condition, the area of АА1С1С is equal to 1400 cm2, then we determine the height of the prism.

Saa1c1c = AC * A1H.

1400 = 70 * A1H.

A1H = 1400/70 = 20 cm.

Determine the area of the base of the rhombus.

Savsd = АС * ВD / 2 = 70 * 24/2 = 840 cm2.

Let’s define the volume of the prism.

V = Sbn * A1H = 840 * 20 = 16800 cm3.

Answer: The volume of the prism is 16800 cm3.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.