Non-Verbal Reasoning by Dr. R S Aggarwal-Analytical Reasoning- Short Trick to Finding no of triangle.

Non-Verbal Reasoning by Dr. R S Aggarwal-Analytical Reasoning- Short Trick to Finding no of triangle.

Here’s a short and effective trick to find the number of triangles in Non-Verbal Reasoning problems — especially from books like “Non-Verbal Reasoning” by Dr. R.S. Aggarwal (Analytical Reasoning section).

Short Trick to Count Number of Triangles

1. Use the Triangle Counting Formula (Straight Line Division)

For a triangle divided by lines from one vertex:

No. of triangles = n(n + 1)/2

Where n is the number of divisions inside the triangle.

Example:
If a triangle is divided into 4 parts from one vertex:
= 4(4 + 1)/2 = 10 triangles

2. Use Layer-Based Count (for Grid/Stacked Triangles)

In stacked or step-triangle figures:

Total triangles = 1 + 3 + 5 + … (odd numbers for each layer)
or
Use formula: n² (where n = number of rows)

Example:
If there are 4 layers (rows of triangles):
Total = 4² = 16 triangles

3. For Complex Figures – Use Zone Method

• Break the figure into zones or blocks

• Count triangles in each zone separately

• Add all, including big triangles formed by combinations

Tip:
Mark each triangle while counting to avoid duplication.

4. For Overlapping Squares or Figures

• Check how many smaller triangles are formed inside each square

• Count the overlapping/intersecting ones

• Count bigger triangles formed by combination of smaller ones

Smart Tip: Use Colors or Labels While Practicing

• Use alphabets like A, B, C… to label corners

• Count small triangles first, then medium, then big

Example from Dr. R.S. Aggarwal (Common Type)

A triangle is divided into 3 parts by drawing 2 lines from the top vertex to the base.
Count each triangle (3 small + 2 medium overlapping + 1 big) = 6 triangles

Practice Examples to Try:

• A star shape (intersecting triangles)

• Pyramid of triangles

• A triangle inside a square

• A figure formed by intersecting diagonals

Would you like:

• A PDF sheet with 25 triangle-counting practice problems?

• Video explanation of the top 5 triangle puzzles?

• A printable formula chart for non-verbal reasoning?

Let me know and I’ll generate it for you.

Non-Verbal Reasoning by Dr. R S Aggarwal-Analytical Reasoning- Short Trick to Finding no of triangle.

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