In an inclined prism, the distance between the lateral ribs is 10,17,21. The lateral rib is 18. Find the volume of the prism.

The area of ​​the inclined prism is equal to the product of the length of the lateral rib and the cross-sectional area parallel to this rib.

Since, by condition, we know the distances between the side edges, these are the lengths of the sides of the triangle in the section parallel to the edge.

By Heron’s theorem, we determine the cross-sectional area A2B2C2.

Ssech = √p * (p – a) * (p – b) * (p – c), glee p is the semiperimeter of the triangle, a, b, c are the lengths of the sides of the triangle.

p = (10 + 17 + 21) / 2 = 24 cm.

Ssection = √24 * (24 – 17) * (24 – 21) * (24 – 10) = √24 * 7 * 3 * 14 = √7056 = 84 cm2.

Let’s define the volume of the prism.

V = Ssection * AA1 = 84 * 18 = 1512 cm3.

Answer: The volume of the prism is 1512 cm3.