__Category__: Solid Geometry"Published in Newark, California, USA"

A vegetable bin built in the form of a cube with an edge of 6 ft. is divided by a vertical partition which passes through two diagonally opposite edges. Find the lateral surface of either compartment.

__Solution__:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life |

If a plane or a divider connects the two opposite sides of a cube, then a cube becomes two triangular prisms with equal bases, lateral surfaces, and their volumes as well.

If the sides of a cube are all equal, then the bases of two prisms are all isosceles right triangles.

Use Pythagorean Theorem in order to solve the another side of the base of a triangular prism which is the hypotenuse as follows

Therefore, the lateral surface area of a triangular prism which is a compartment of a vegetable bin is

or