11. (5 points) As shown in the figure, the "L" shaped paper piece with a perimeter of 52 centimeters can be divided into two identical rectangles along the dotted line. If the longest side is 16 centimeters, then the area of the "L" shaped paper piece is $\qquad$ square centimeters.
【Analysis】According to the problem, let's assume the width of the divided rectangle is $x$ cm, then the length of the divided rectangle should be (16-x) cm. By adding the perimeters of the "L" shaped paper pieces, we can get an equation: $16+(16-x)+x+(16-x-x)+(16-x)+x=52$. After solving this equation, we can find the width of the divided rectangle, then substitute $16-x$ to calculate the length of the divided rectangle, and finally calculate the area of the rectangle to get the answer.

【Solution】Solution: Let the width of the divided rectangle be $x$, then the length of the divided rectangle is $16-x$,
$$
\begin{array}{l} 
16+(16-x)+x+(16-x-x)+(16-x)+x=52 \\
64-2 x=52, \\
2 x=12, \\
x=6,
\end{array}
$$

The length of the divided rectangle is: $16-6=10$ (cm), the area of the rectangle is: $10 \times 6=60$ (square cm), the area of the "L" shaped paper piece is: $60 \times 2=120$ (square cm).

Therefore, the answer is: 120.