The topic comes from the weekly measurement of polygon area in the fifth grade unit of primary school mathematics. The side length of the big square is 5 cm, the area of the small square is 3 cm, and the area of the shaded part is 9.5 cm.

This topic requires us to find out the area of the shadow by calculation. First of all, we can see that the side length of the big square is 5 cm, the area of the small square is 3 cm 2, and the area of the shadow is 9.5 cm 2.

We can calculate the area of the shadow part by steps: first, calculate the area of the big square with the square of the side length, that is, 5×5=25 square centimeters. Then calculate the area of the small square, which has been given as 3 square centimeters. Then, we halve the area of the big square, that is, 25÷2= 12.5 square centimeters.

We add half the area of the big square to the area of the small square, and then subtract the area of the blank right triangle (the area of the right triangle with a base length of 5 cm and a height of 3 cm) to get the area of the shadow part.

Specific calculation process: shaded area = half of large square area+small square area-right triangle area in blank = 5× 5 ÷ 2+3× 3-(5+3) × 3 ÷ 2 =12.5+9-12 = 9.5 square centimeters. Therefore, the shadow area is 9.5 square centimeters.

Method for calculating the area of shadow part:

1, direct calculation method: if the shadow part is a regular geometric shape, such as rectangle, square, triangle, etc. The area can be directly calculated by geometric formula. For example, if the shadow part is rectangular, the area can be calculated by the product of length and width; If it is a triangle, the area can be calculated by half of the product of the base and the height.

2. Difference calculation method: If the shadow part is in the overlapping area of two or more graphs, the area of the shadow part can be obtained by calculating the difference between the areas of two or more graphs. For example, if there is a big square and a small square, and their shadow part is the overlapping part of a small square in the big square, the area of the shadow part can be calculated by subtracting the area of the small square from the area of the big square.

3. Proportional calculation method: If the shadow part is a complex irregular figure, but the size and proportion of the whole figure are clear, the area of the shadow part can be calculated by proportional calculation method. For example, if a part of an image is covered, the area of the covered part can be calculated by the proportional relationship between the uncovered part and the whole image.

4. Coordinate calculation method: If the shadow part is in two-dimensional or three-dimensional coordinate system, the area of the shadow part can be obtained by coordinate calculation method. For example, in the two-dimensional coordinate system, the area of the shadow part can be calculated by solving the equation of the boundary curve of the shadow part; In the three-dimensional coordinate system, the volume of the shadow part can be calculated by solving the surface equation of the shadow part.