How many triangles are there in the figure PQRS given below? [Figure: Rectangle PQRS divided into multiple triangles]

Question

How many triangles are there in the figure PQRS given below?

[Figure: Rectangle PQRS divided into multiple triangles]

1. A. 16
2. B. 10
3. C. 18
4. D. 12 (Correct answer)

Correct Answer

Option D — 12

Detailed Solution & Explanation

The correct answer is 12.

Key Points

• This is a figure-counting reasoning question in which all the triangles formed within the rectangle PQRS — including the small individual triangles and the larger triangles made by combining them — must be counted systematically.
• Counting carefully by size (first the smallest triangles, then those formed by joining two or more smaller ones), the total number of triangles in the figure comes to 12, which matches option (D).

Exam Tip

• for 'how many triangles' figures, never count randomly — label every point, count all the smallest triangles first, then the two-part and larger composite triangles in order.
• This systematic method prevents both double-counting and missed triangles that lead to wrong options.

Additional Information

• Count triangles systematically by size — first the smallest, then those made of two components, then three, and so on — rather than scanning the figure at random.
• The total is the sum across all sizes; missing the large composite triangles that span the whole figure is the most common error.
• Related counting questions use the same discipline for squares and rectangles: for an m×n grid the rectangle count is mC2 × nC2 using the grid lines.