The royal road to mathemathics

Puzzle

Again I am forced to tell your Imperial Highness that the royal road to geometry has not yet been discovered,' exclaimed Euclid to King Ptolemy, who had been dozing during a lecture on the elements of geometry. "To illustrate the futility of knocking learning into a pupil's skull with a wormwood club," said Beppo, the court jester, "I make bold to volunteer a few soothing remarks. "My learned friend has discoursed upon the six geometrical forms, the traprapezium, the square, greek cross, parallelogram or diamond, rectangle and triangle. The trapezium, he has told us is a geometrical form with four sides, no two of which are parallel. The shape was originated many years ago as the mainsail for a catamaran, the five other geometrical shapes will readily be recognized as the flags or ensigns of ancient yachts. The most interesting part of the whole business is that I can mark off the trapjezium into five parts, which form six wonderful puzzles. Cut these five pieces out of paper and it will be no easy task to rearrange them to form the trapezium. Then utilize all five of the pieces so as to form a perfect square! They will also fit together to make a greek cross. If properly placed they will make a perfect parllelogram, or a rectangle, or a right angled triangle.
"Thus we have the six geometrical shapes illustrated by these five magical pieces, and it is safe to say that by the time you have guessed these six puzzles you will be pretty familiar with the geometrical form, and won't have gone to sleep over Euclid's eleven volumes either! All of the five pieces must be utilized in producing each of the patterns shown, just as in the case of the trapezium, and will go far towards teaching the mystic affinity or relationship between the different geometrical forms as treated by ancient occult writers."

Puzzle in short

Cut the shape shown in the picture (a trapjezium) into five pieces. Then form a trapjezum, a perfect square, a greek cross, a perfect parallelogram, a rectangle, and a right angled triangle from the pieces.

Answer

References

• Loyd, Sam [1914]. in Loyd, Sam, Jr.: Sam Loyd's Cyclopedia of 5000 Puzzles Tricks and Conundrums (in English). New York: Lamb Publishing company, page 60.