Chapters

Page 2

Q3). Find the number of Triangle in following Square figures?

Answer

Let’s start with the short trick directly

(i)

Short Trick:

 In this types of figures count the number of parts and multiply by 2

 I.e. here number of parts is 4

 4 × 2 = 8 is the ans.

 

(ii)

Short Trick:  

Here number of parts is 6

 6 × 2 = 12 is the ans.

 

(iii)

Short Trick:

Here number of parts is 8

8 × 2 = 16 is the ans.

 

(iv)

  1. Divide the figure into separate individual part.
  2. When two figures merged, find out the common portion too, it may be possible that common part will increase the number of triangles. Here BE is the common portion and because of that we can get two more triangles i.e: 

            △AEC and △FBD  

            16+2=18 triangles Ans.

 

(v)

 b). More triangles due to common intersection.

  △AGC  + △DBH  + △BDF   + △CHE    + △AEC =5

  Total no of  △ = 24+5 = 29

 

(vi)

  1. Four different individual can make 8*4=32 triangles(as shown in previous question).
  2. More triangles due to common intersection.

    △AOC  + △COE  + △EOG  + △GOA   + △HBD  + △BDF  + △DFH   + △BHF = 8

  3. More triangles formed with these 8 triangles(from step B).

    △EGA + △GAC   + △ACE   + △CEG =4 

    Total no of  △ = 32+8+4 = 44


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