A deceptively simple question setup leads to a number of attack methods and a surprisingly sophisticated solution set in this open-ended problem. Young geometers of different strengths can go about defining the solutions graphically,...

A challenging proof like geometry of finding the square inscribed in a triangle.

A geometry problem of finding the area of a sloped square within a square.

A "three star" geometry problem requiring some prior knowledge in math and proofs to maximize the area of an inscribed triangle in terms of the hypotenuse.

A problem of finding the fraction of a square that is shaded given criterion. Students will have to use their mathematical reasoning and triangle solving skills to solve this area problem.