159 The area enclosed by the curve $(|x|-1)^{2}+(|y|-2)^{2}=5$ is $=$

The area enclosed by the curve $(|x|-1)^{2}+(|y|-2)^{2}=5$ is $=$
$15910 \pi+16$. As shown in Figure 15, the area enclosed in the first quadrant is the part of the circle $(x-1)^{2}+(y-2)^{2}=5$ in the first quadrant, its area
$$
=\frac{1}{2} \times \pi \times 5+\frac{1}{2} \times 2 \times 4=\frac{5}{2} \pi+4 .
$$

The required area $=4\left(\frac{5}{2} \pi+4\right)=10 \pi+16$.