[math]c^2[/math]

[math]a^2+b^2[/math]

Each triangle that appears has area [math]\frac{1}{2}ab[/math].[br]The yellow/green square visible in the middle of the transformation has area [math]\left(a+b\right)^2=a^2+2ab+b^2[/math].[br]The yellow rectangles visible at the end have area [math]ab[/math].