If you look closely, you will know that the long sides of the two large triangles are not straight lines, the long sides of the upper triangle are concave downward and the lower triangle is convex upward. This is the area difference, and the whole effective area should be 32. Because the green and red triangles are not similar triangles at all, similar to the green triangle, when the short side is 3, the long side should be 7.5 instead of 8.

Responder: skbbb- Jianghu Shaoxia level 6 5-7 12:50

The picture is wrong. Try it yourself.

Respondents: Aring Zhang zhp- Jianghu rookie level 5 5-7 12:5 1.

For the convenience of description, each block is named: red triangle: r; Dark green triangle: b; Green long block: g; Long yellow square: y.

The area of each department in the following figure is the same as that in the above figure, calculated as: R- 12 (grid); b-5； y-7； G8. But the total area of the upper and lower graphs is 32.5 (the triangle area is length * height *0.5), and there is a difference of 0.5 in the middle, which is the extra white square.

The specific source of the white square: G and Y in the above figure form a rectangle with an area of15; The figure below shows 16, but actually Y+G is only 15.

Interviewee: He Yimin-Assistant Level 3 5-7 12:59.

It's an illusion, because the way you look is actually different because of the edge.

Respondent: Waiting _ Spirit-Assistant Level 2 5-7 17:44

The area is absolutely equal. This is because this figure actually takes advantage of people's visual differences. In other words, the hypotenuse of the triangle above is a straight line, but in the picture below, the hypotenuse is neither a straight line nor five units high.

If you have done your own experiment, I suggest you make the drawing strictly according to the graphic requirements, because this error comes from small gaps in all aspects, so you can't see the sketch. When finished, you can measure it. Suppose that the base of the original triangle you made is 13cm and the height is 5cm, then you can measure the height of the figure you later put together to ensure that it is longer than 5cm, or you can compare the hypotenuse with a ruler, which is definitely not in a straight line. If you continue to cut paper according to your experiment, and the area remains the same, you can simply cut it every day, and you can get a large pile of paper without losing the area, so you don't have to cut trees to make paper, which is a great contribution to environmental protection.

This result can also be verified by proportional calculation:

On the whole, the ratio of the base to the height of the big triangle in the above figure is 13: 5, so from the scale analysis, it can be seen that the base of the red triangle and the green triangle are 8 units and 5 units respectively, so from the proportion of similar shapes, it can be known that the height of the red triangle should be 40/ 13, while the height of the green triangle should be 25/ 13.

Then calculate the heights of yellow and light green. The height of the rectangle formed by the superposition of the two figures in the above figure should be the same as that of the red triangle, both of which are 40/ 13 units. However, due to the change of combination mode, the height of the new figure in the following figure should be 2/3 of the rectangle combined in the above figure, so the height of the new figure is 80/39 units. This height plus the height of the red triangle is the height of the big triangle in the picture below, and the result should be 40/65433.

Because the new figure height of the yellow and light green figure combination in the following figure is known as 80/39, if the hypotenuse is on a line according to the visual feeling in the following figure, then this height should be equal to the height of the green triangle, but in fact the height of the green triangle is 25/ 13, which is 75/39, and there is an error of 5/39 between them. How can the hypotenuse be a straight line?

With so many mistakes, you will find that your eyes have deceived you. It can even be pointed out that even the extra small space is not 1 square unit through accurate calculation, and there is an error in it. Those who are interested can be calculated by calculation.

Respondent: Koygu-Juren Grade 4 5-9 12: 16.