13. (15 points) As shown in the figure, squares $a$, $b$, $c$, $d$, and $e$ are used to form a rectangle that is 30 cm long and 22 cm wide. Find the area of square $e$.
【Analysis】According to the problem, we can use the sum of the side lengths of the connected shapes to find the side length of $e$, and then calculate the area.
【Solution】Solution: According to the analysis, the sum of the side lengths of squares $a$, $b$, and $c$ is $30$ cm,
the sum of the side lengths of squares $a$ and $b$ is $22$ cm,
$\therefore$ the side length of square $c$ is: $30-22=8$ cm;
Also, $\because$ twice the side length of square $c$ plus the side length of $e$ is $22$ cm;
the side length of square $e$ is $22-8 \times 2=6$ cm;
Therefore, the area of square $e$ is: $6 \times 6=36$ square cm.
Answer: The area of square $e$ is 36 square cm.