I will be thankful for any ideas and clues

Darya

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Jan 17, 2020
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We have a cube ABCDEFGH. M, N, R, S are middle points of AB, AD, EF, FG. Planes MRN, BFH, BDS divide the cube into 4 polygons. The problem is to find the ratio between their volumes.
Do I actually have to find the volume of each polygon? Is there maybe another faster way to solve this? Thanks a lot!
 

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Volumes of prisms with the same height are proportional to their bases. That's where I'd start, though parts of this will take a little more thinking, perhaps multiple steps using extra planes.

Presumably you copied "polyhedra" as "polygons" by mistake.
 
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