Two squares with a side length of 8 cm are overlapped and spliced together, so that the perimeter of the shaded part in the figure is 20 cm, and the perimeter of the spliced large rectangle is 44 cm.

We have two squares with a side length of 8 cm, stacked together. We know that the circumference of the shadow part is 20 cm. Our task is to find the perimeter of the stacked rectangle.

Suppose that the length of the big rectangle after splicing two squares is l cm and the width is w cm. According to the topic, we can know that the side length of two squares is 8 cm, so the length of the spliced rectangle is l=8+8= 16 cm.

The perimeter of the shaded part is 20 cm, which consists of half the length and twice the width of two squares. Therefore, 2×(8/2)+2×w=20. W=(20-8)/2=6 cm. Now that we know the length and width of the big rectangle, we can calculate its circumference. The result of calculation is that the circumference of the big rectangle is 44 cm.

This topic can also put the problem into a coordinate system, which can help us intuitively understand the situation of overlapping boxes. By setting appropriate coordinate system and marking key points, complex problems can be simplified and solved more easily.

Mathematical skills of overlapping squares;

1. Understand the meaning of the topic: Make sure you have fully understood the topic. Including understanding the graphics involved in the topic, giving data and problems to be solved.

2. Determine the known quantity and unknown quantity: specify the numerical value, unit and unknown quantity to be solved in the topic. This will help you clearly understand the problems that need to be solved and determine the strategies to solve them.

3. Identify geometric features: A square has some specific geometric features, such as four equilateral sides and four right angles. When solving mathematical problems involving squares, we must make full use of these characteristics.

4. Using mathematical model: according to the specific problems of the topic, choose the appropriate mathematical model. This may include algebraic equations, trigonometric functions, calculus, etc. Using the right model can help you solve problems more effectively.

5. Perform calculation: calculate and solve the unknown quantity according to the mathematical model you choose and the known data. Make sure that your calculation process is accurate, and it is best to check it several times to avoid possible mistakes.

6. Integrate the answers: Integrate your calculation results to make sure the answers are clear. If necessary, you can draw a chart or make other visual tools to help explain the answer.