Notes
square overlapping a square and a rectangle solution

Solution to the Square Overlapping a Square and a Rectangle Puzzle

Square Overlapping a Square and a Rectangle

The area of the largest square is 2525. What’s the combined area of the smaller square and rectangle?

Solution by Invariance Principle

Square overlapping a square and a rectangle special case one

The angle of the larger square can be varied. When it is aligned horizontally, the outer square and the darker blue square coincide (meaning that the lighter blue rectangle effectively does not exist) showing that they have the same area.

Square overlapping a square and a rectangle special case two

Alternatively, if the larger square is tilted at 45 45^\circ to the horizontal then the lighter blue rectangle is also a square and the two shaded squares have the same combined area as the outer square.