In a cube with a base side 6, a section is drawn through the side of the lower base and the middle of the opposite face.

In a cube with a base side 6, a section is drawn through the side of the lower base and the middle of the opposite face. Determine the total area of the prism cut off by the plane from the cube.

Find the area of ​​a triangular prism cut off from the cube;

According to the condition of the task, we are given a cube with a known side, and a prism is given, which is cut off from this cube.

Since the plane cutting off the prism passes through the middle of the opposite side, then one side of the triangular prism will be equal to:

6/2 = 3;

Knowing the side of the cube, we also know the second side of the triangular prism 6.

And since all sides of the cube are equal, it means that the height of this prism is also equal to 6;

Let’s write the formula for the volume of the prism;

V = S * h;

Since the triangle at the base of the prism is rectangular then;

S = a * b = 6 * 3 = 18;

Knowing the base area, we find the volume;

V = 18 * 6 = 108.