7. (10 points) As shown in the figure, a square is divided into 4 identical rectangles, and the perimeter of each rectangle is 20 cm. Then the area of this square is $\qquad$ 64 square cm.
【Analysis】To find the area of this square, we should first determine the side length of the square. From the given conditions, we know that the width of the small rectangle is $\frac{1}{4}$ of its length. Using the perimeter formula for a rectangle, we can find its length, which is also the side length of the square.

【Solution】Let the side length of the square be $x$,
$$
\begin{aligned}
\left(x+\frac{1}{4} x\right) \times 2 & =20, \\
\frac{5}{4} x \times 2 & =20, \\
\frac{5}{4} x & =10, \\
x & =8,
\end{aligned}
$$

Thus, the area of the square is $8 \times 8=64$ (square centimeters);
Answer: The area of the square is 64 square centimeters.
Therefore, the answer is: 64.