10. In the complex plane, region $A$ consists of points $Z$ corresponding to complex numbers $z$, if the real and imaginary parts of $\frac{z}{40}$ and $\frac{40}{z}$ are both between 0 and 1, find the area of $A$.
10. Let $z=x+i y, x_{1}, y \in \mathrm{R}$, then
$$
0 \leqslant x \leqslant 40,0 \leqslant y \leqslant 40 \text {. }
$$

Also, $\frac{40}{z}=\frac{40 x}{x^{2}+y^{2}}+i \frac{40 y}{x^{2}+y^{2}}$, thus
$$
0 \leqslant \frac{40 x}{x^{2}+y^{2}} \leqslant 1,0 \leqslant \frac{40 y}{x^{2}+y^{2}} \leqslant 1 \text {, }
$$

which means $\left\{\begin{array}{l}(x-20)^{2}+y^{2} \geqslant 20^{2} \\ x^{2}+(y-20)^{2} \geqslant 20^{2}\end{array}\right.$
From (8), (9), and (10), we know that region $A$ is the shaded part in the above figure, hence the area of $A$ is $S=1200-$ $200 \pi$.