11. (12 points) As shown in the figure, a large rectangle is divided into 8 smaller rectangles, where the perimeters of rectangles $A$, $B$, $C$, $D$, and $E$ are 26 cm, 28 cm, 30 cm, 32 cm, and 34 cm, respectively. What is the maximum area of the large rectangle in square centimeters?
11. (12 points) As shown in the figure, a large rectangle is divided into 8 smaller rectangles. The perimeters of rectangles $A$, $B$, $C$, $D$, and $E$ are 26 cm, 28 cm, 30 cm, 32 cm, and 34 cm, respectively. What is the maximum area of the large rectangle in square centimeters?
【Solution】Let the height of $B$ be $a$, then the heights of $A$, $C$, and $D$ are $a-1$, $a+1$, and $a+2$, respectively. The width of $B$ is $28 \div 2 - a = 14 - a$, and the width of $E$ is $14 - a + 3 = 17 - a$,

The area of the large rectangle is $(a-1 + a + a+1 + a+2)(14-a + 17-a) = (4a + 2)(31 - 2a) = 2(2a + 1)(31 - 2a)$,
$2a + 1$ and $31 - 2a$ sum to 32, and the product is maximized when the two numbers are as close as possible,
$$
2a + 1 = 31 - 2a, 4a = 30, a = 7.5,
$$

The total area is $2 \times 16 \times 16 = 512$ square centimeters.
Therefore, the answer is 512.