Back to the entrance examination of management, plane geometry is also an unavoidable topic, and its common methods include finding side length, perimeter and area, among which finding the shadow area of plane geometry is a very important test point. This kind of topic can better examine the examinee's ability to read pictures and comprehensive knowledge of mathematics, so this kind of topic is more flexible, and many students can't start when they see this kind of topic. Here @ Xinquan Lecture Hall-Liao Wei used several examples to help friends master the solutions to such problems.
Through the analysis of real problems over the years, there are two methods to find the shadow area of plane geometric figures: one is to find the area of regular figures (such as triangles, rectangles, trapezoid, sectors, etc.). ); The second is to find the area of irregular figure. For the former, the area formula can be directly applied to find its area, which is relatively simple, so I won't go into details here. For the latter, it needs to be transformed into the area problem of regular graphics, and its solutions include sum and difference method, equal product method, digging and filling method, equation method and so on.
Skill one sum difference method
Principle: Through observation, we can analyze which regular patterns are composed of irregular patterns, and then use the sum or difference of these regular patterns to find them, thus simplifying the complex.
Example 1. As shown on the right, the radius of the inscribed circle of a square is r, and this square divides its circumscribed circle into four bows. What is the total area of these bows?
Skill two-cut complement method
Principle: Cut off a part of a figure and move it to another suitable position, thus forming a figure with an easy-to-find area. Example 2. As shown on the right, ABCD is a square with an area of 1, and △PBC is a regular triangle. △ What is the area of △PBD?
Skill three-equation method
Principle: According to the characteristics of shape and size, figures are classified, and the areas of different figures are represented by unknowns, and the shadow areas are solved by establishing equations.
Example 3. As shown on the right, the centers of the four circles are the four vertices of the square, and their common point is the center of the square. If the radius of each circle is 2 cm, what is the area of the shadow?
I believe that when solving this kind of problem, as long as the friends thoroughly examine the problem and analyze the specific problems, they will definitely find a reasonable, concise and appropriate solution.