JAMIA 2024 — Reasoning PYQ

Counting

We can divide the figure into three main sections: the Left wing, the Middle square/rectangle, and the Right wing.

1. Small Individual Triangles:

These are the smallest single-unit triangles visible in the diagram.

• Left Wing: $1$ triangle.

• Middle Section: There are $6$ small triangles created by the intersecting diagonal and vertical lines.

• Right Wing: $1$ triangle.

  $$\text{Total Small}=1+6+1=8$$

2. Triangles formed by combining 2 components:

• Left Side: The combination of the left wing and the first vertical part of the square creates $1$ larger triangle.

• Middle Section: Combining adjacent small triangles inside the square creates $2$ larger triangles (split by the diagonal).

• Right Side: The combination of the right wing and the right vertical part of the square creates $1$ larger triangle.

  $$\text{Total Medium}=1+2+1=4$$

3. Triangles formed by combining 3 or more components:

• Looking at the overall structure, there are $2$ large triangles formed by the diagonal line spanning across the middle section and including the base.

  $$\text{Total Large}=2$$

Mathematical Representation

Let $T$ be the total number of triangles:

Substituting the values:

Answer: There are 14 triangles in the given figure.