When proving the Pythagorean Theorem, the area of the big square is the sum of the area of the small square and the four small congruent right triangles
The calculations used to prove the Pythagorean Theorem can be presented as follows;
Please see the attached diagram of the large square ABCD and the smaller square EFGH, created with MS Word
Area of the big square ABCD = (a + b)²
Area of the 4 triangles is; 4 × (1/2) × a × b = 2·a·b
Area of the small square EFGH is; c²
Area of the big square is therefore;
(a + b)² = c² + 2·a·b
a² + 2·a·b + b² = c² + 2·a·b
The like terms on both sides of the equation indicates that we get;
a² + b² = c² (Pythagorean Theorem)