# Unit cube cut into two parts through its diagonals

Question:

A cube having each side of unit length is cut into two parts by a plane through two diagonals of two opposite faces. What is the total surface area of each of these parts?

My attempt:

I am still unable to visualize the problem, let alone solve it! I have managed to solve similar problems involving spheres because visualizing spheres was easy but this is (very) tough.

Can someone please give starting hints?

UPDATE: I agree with Ross's answer, but it took me a whole while to visualize this thing. Now that I do visualize, it would be great if everyone like me could visualize.

I would wish if someone could please simply draw a diagram to illustrate the problem. I don't have sharp skills with 3D math geometry software otherwise I would do that myself.

• Have you tried drawing a picture? Have you tried taking a cube (say, a die) and marking its outside with a marker to show where the cut goes? Have you tried making a cube out of fruit and cutting it in the required way? – MJD Apr 18 '16 at 16:04

The result of the cut is two right triangular prisms. The base of each is a $1-1-\sqrt 2$ triangle (the result of cutting one face of the cube) and the height is $1$