This week's maths problem

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Problem of the week

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On Friday of each week we will post a new maths challenge.
You may submit your solution by the following Thursday.
Each problem contains two different levels of difficulty. You will be awarded from 2 to 12 points for a full answer.
Each series contains 12 problems before the stage winner is determined.
Your score will be published here.

In each series we will give away 3 books as prices. The prices will be drawn by lot among the best ten participants of the series. The books are kindly sponsored by Buchdienst Rattei of Chemnitz.

Suggestions for problems are welcome.

Deadline is 3nd of December 2020.

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Series 55

problem 656

“That’s a nice figure, that you’ve drawn.”, Mike told Bernd. “Yes, I like it too, although I had a different one before, beginning with a cube instead of the prism ABCDEF.”, answered Bernd.
If the figure in the middle is a cube (a =10 cm) and all side areas, which are visible, should have the same area, how big would the face and the volume of the newly formed figure be? (2 + 4 points)
How big are face and volume of the pictured figure, if AB =BS₂=AS₂ = a = 10 cm and the area of all visible side areas have to be the same size? - 6 red points

-> Enigma <--

https://www.schulmodell.eu/images/stories/mathe/horst/raetsel.php

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adress:
Thomas Jahre
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