Methods 1: geometric analysis
Using symmetry: If the number graph is symmetrical, we can use the symmetry property of the graph to find the number of trapeziums. For example, if the center of a graph is symmetrical, the number of trapezoids in another part can be inferred by observing one symmetrical part.
Decompose into small blocks: decompose a complex figure into smaller parts, analyze and calculate the number of trapezoid in each small part, and then sum.
Method 2: Counting rules
Rule of permutation and combination: Use the idea of permutation and combination to calculate the number of trapezoid. According to the characteristics of the figure, considering the connection mode of adjacent line segments or points, the number of possible trapezoid is calculated by permutation and combination method.
Recursive or inductive method: observe the law and calculate the number of trapezoid by recursive or inductive method. Start with small-scale figures and gradually expand to a larger scale, and find a regular change law.
Method 3: classified discussion
Classification according to specific properties: according to the properties of several graphics (such as the direction, length and angle of line segments, etc. ), classify the graphs and calculate the number of trapeziums for each case.
Geometric figure analysis: observe the special geometric shapes in the number diagram, such as triangles and parallelograms, and deduce the number of trapezoid by using their relationship.
Method 4: Graph Segmentation and Reorganization
Graph segmentation: divide the region in the graph into smaller parts, which may make it easier to calculate the number of trapeziums.
Graph recombination: to recombine or rearrange the graphs in several graphs in order to better identify and calculate the number of trapezoid.
Method 5: Mathematical model
Establish a mathematical model: if the characteristics of the number graph are clear, a mathematical model can be established to describe the graph structure, and then the number of trapezoids can be calculated mathematically.
Using algebraic or geometric methods: using algebraic equations or geometric theorems to solve the number of trapeziums, and transforming the characteristics of graphics into mathematical expressions for calculation.