12. As shown in the figure, the perimeters of two squares differ by 12 cm, and their areas differ by 69 square cm. The areas of the larger and smaller squares are $\qquad$ square cm, $\qquad$ square cm.
【Answer】169 square centimeters, 100 square centimeters
【Key Points】Perimeter and area of a square, Difference of squares formula
【Analysis】
Let the side length of the larger square be $a$ centimeters, and the side length of the smaller square be $b$ centimeters. According to the problem, we have:
$\left\{\begin{array}{c}4 a-4 b=12 \\ -b=69\end{array}\right.$, which simplifies to $\left\{\begin{array}{l}a-b=3 \\ (a+b)(a-b)=69\end{array}\right.$, or $\left\{\begin{array}{l}a-b=3 \\ a+b=23\end{array}\right.$;
Solving, we get $\left\{\begin{array}{l}a=13 \\ b=10\end{array}\right.$, so the area of the larger square is $13^{2}=169$ square centimeters, and the area of the smaller square is $10^{2}=100$ square centimeters.