Answer :

The pieces fit together as in Diagram 1, Diagrams 2 and 3 showing how the two original squares are to be cut. 
It will be seen that the pieces A and C have each twenty chequers, and are therefore of equal area. 
Diagram 4 (built up with the dissected square No. 5) solves the puzzle, except for the small condition contained in the words, "I cut the two squares in the manner desired." 
In this case the smaller square is preserved intact. 
Still I give it as an illustration of a feature of the puzzle. It is impossible in a problem of this kind to give a quarter-turn to any of the pieces if the pattern is to properly match, but (as in the case of F, in Diagram 4) we may give a symmetrical piece a half-turn—that is, turn it upside down. 
Whether or not a piece may be given a quarter-turn, a half-turn, or no turn at all in these chequered problems, depends on the character of the design, on the material employed, and also on the form of the piece itself.

Math Genius