In an inclined prism, the distance between the side ribs is 37 cm, 13 cm
In an inclined prism, the distance between the side ribs is 37 cm, 13 cm and 40 cm. The side rib is 5 cm, find the area of the side surface 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), where p is the semiperimeter of the triangle, a, b, c are the lengths of the sides of the triangle.
p = (13 + 37 + 40) / 2 = 45 cm.
Ssection = √45 * (45 – 13) * (45 – 37) * (45 – 40) = √45 * 32 * 8 * 5 = √57600 = 240 cm2.
Let’s define the volume of the prism.
V = Ssection * AA1 = 240 * 5 = 1200 cm3.
Answer: The volume of the prism is 1200 cm3.