Every one has his/her own counting strategy when counting the number of geometry shapes.

Below are some common strategies.
• For simple shapes, an easier way is to permute all the combination.

  Example 1

  1.  How many different line segments can you count in the following figure?

  
  

  Your Answer:

  [Correct Answer]:3

  Hint:
• For more complex shapes, a good idea is to first figure out the pattern and then counting (calculating) based on the pattern.

  Example 2

  1.  How many different line segments can you count in the following figure?

  
  

  Your Answer:

  [Correct Answer]:15

  Hint:

  Example 3

  2.  How many triangles can you count in the following figure?

  
  

  
  

  Your Answer:

  [Correct Answer]:56

  Hint:

  3.  How many rectangles can you count in the following figure?

  
  

  
  

  Your Answer:

  [Correct Answer]:45

  Hint:

  (1 + 2)(1 + 2 + 3 + 4 + 5)