By the diagram show, we can state that:
Equations for areas would be:
[tex]\begin{gathered} Abigsquare=(a+b)^2 \\ A_{4triangles}=4(\frac{1}{2}ab) \\ A_{whitesquare}=big\text{ square- 4 shaded triangles} \end{gathered}[/tex]
Then,
For the area of the white square:
[tex]A_{whitesquare}=(a+b)^2-4(\frac{1}{2}ab)[/tex][tex]\begin{gathered} A_{whitesquare}=a^2+2ab+b^2-2ab \\ A_{whitesquare}=a^2+b^2 \end{gathered}[/tex]
