The diagonal section of a regular hexagonal prism divides it into 2 unequal parts.

The diagonal section of a regular hexagonal prism divides it into 2 unequal parts. Find the ratio of the side surfaces of these parts.

Let’s draw the base of a regular hexagonal prism – this is a regular hexagon. If our section divides the base into unequal parts, then it will look like in the figure. If the parts were equal, then the section would pass along the blue line.

In one section we have 2 side faces, and in the other – 4. The area of the 4 faces S1 = 4ah (a is the side of the base, h is the height of the prism).

The area of 2 sides S2 = 2ah.

S1 / S2 = 4ah / 2ah = 4/2 = 2/1.

Answer. S1: S2 = 2: 1.