Problem 1007

You can discover here the projection of a coffee capsule and its case.



The capsule is projected on a trapezium of small base 16 mm, the other three sides having a length of 32 mm each. The trapezium is inscribed in a square: the projection of the wrapping. The packaging designer managed to save cardboard by reducing the side of the square according to the figure: square and trapezium have a common vertex, two other vertices of the trapezium touching the sides of the square.

• 1A. What is the length of a diagonal of the trapezium in mm?
  
  
• 2A. What is, in mm², the area of the square?
  
  

I haven't made any program for this problem.

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