7. In the complex plane $\left\{\begin{array}{l}0 \leqslant \arg (z-1) \leqslant \frac{\pi}{4},(\operatorname{Re}(z) \text { represents the real part of } z) \text { the points that form the corresponding figure have an area of } \\ \operatorname{Re}(z) \leqslant 2\end{array}\right.$ . $\qquad$
7. $1 \quad S=\frac{1}{2} \times 2 \times 1=1$