Find the area of the shaded zone

Consider the diagram. The whole area is equal to the area of the $19 \times 19$ square minus the area of the four triangles. We have

$\text{whole area}=19^2-4\left(\dfrac{1}{2}\right)(8)(8)=233$

The area of the shaded zone is equal to the whole area minus the area of the squares. We have

$\text{area of shaded zone}=233-4(3^2)-4(4^2)-5^2=$ $\boxed{108}$