The solutions produced here by school students show eight different methods. Reflection on these methods will help other students to see something of the 'bigger picture' in a way they will not experience from ploughing through the syllabus and working from textbooks (although that is also absolutely necessary).

Eight distinct proofs were given to this problem by two students, Alex and Neil (Madras College) using respectively sines, cosines, tangents, vectors, matrices, coordinate geometry, complex numbers and pure geometry.

See Alex and Neil's solution here.

Alex and Neil went on to generalise this problem to rectangles with dimensions $n$ by 1.

See 'Why Stop at Three by One?'