7. Cut a 7-meter long iron wire into two segments (it can also be directly cut into two segments), so that the difference in length between these two segments does not exceed 1 meter. If these two segments are used to form two circles respectively, then the maximum value of the sum of the areas of these two circles is $\qquad$ square meters.
7. $\frac{25}{4 \pi}$.

Let the lengths of the two segments be $x$ meters and $y$ meters, respectively. Then $x$ and $y$ satisfy the following relationships:
$$
\left\{\begin{array}{l}
x>0, \\
y>0, \\
x+y \leqslant 7, \\
|x-y| \leqslant 1 .
\end{array}\right.
$$

The planar region is the shaded part shown in Figure 4. The sum of the areas of the two circles is $S = \frac{x^2 + y^2}{4 \pi}$. Viewing this as the equation of a circle, $S$ reaches its maximum value of $\frac{25}{4 \pi}$ square meters when the circle passes through point $A(4,3)$ or $B(3,4)$.