These puzzles explore how shapes with equal area can be cut and rearranged. They build geometric intuition for area equivalence and set the stage for later links to the Pythagoras theme.
1. Cut a 1 × 5 rectangle into 5 parts and rearrange them into a square.
2. Cut a 5‑cell cross into parts and rearrange them into a square.
3. Cut a 7 × 7 square:
a) into a 4 × 4 square, a 3 × 3 square, and four congruent right triangles;
b) into one square and four congruent right triangles.
4. Prove that any two squares can be cut into parts and rearranged to form one larger square.