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 19nd. June 2025

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Series 69

problem 826

Thanks for the idea to G. Palme.

If you draw the five diagonals in a regular pentagon, you get another pentagram.
Maria and Bernd's grandfather came with a drawing and said: ‘At the beginning of December last year, I bought a star in a garden centre that was glued together from wooden strips and whose outline has the shape of a pentagram. For the points of the star
The following applies to the points of the star: AF = BF = BG = ... = JA = 8 cm = a. I had also taken a photo, but I don't have it with me now, but I do have a suitable drawing!’
How can the length of the diagonals of the pentagon ABCDE be calculated, if possible without using a ready-made formula? [5 blue points]
What is the area of the pentagram? [5 red points]

(A second task about the bought star will be avaible in December 2025.)

Deadline for solution is the 19th. June 2025.

-> Enigma <--

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

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adress:
Thomas Jahre
Paul-Jäkel-Straße 60
09113 Chemnitz
Germany

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