Through the center line of the base of the triangular prism, the volume of which is 80

Through the center line of the base of the triangular prism, the volume of which is 80, a plane is drawn parallel to the lateral rib. Find the volume of the clipped triangular prism.

The volume of the prism is equal to the product of its base and the height.

The cut-off portion has the same height as the plane is parallel to the lateral rib;

Find how many times the area of ​​the cut triangle is less than the area of ​​the base;

Base area S = a * h / 2, where a is the side of the triangle, h is its height;

Since the base of the cut-off triangle is the middle line of the base of the prism, the area of ​​the cut-off triangle is (a / 2 * h / 2) / 2 = a * h / 8, that is, it is 4 times less than the area of ​​the base of the prism;

Since the height of the prism and the cut-off part are the same, the volume of the cut-off part is 4 times less than the volume of the prism and is equal to 80/4 = 20 cm ^ 3.