How many triangles can be identified in the given figure?

Question

How many triangles can be identified in the given figure?

1. A. 24 (Correct answer)
2. B. 29
3. C. 21
4. D. 26

Correct Answer

Option A — 24

Detailed Solution & Explanation

The correct answer is 24.

Key Points

• The figure is a tall rectangle made of two stacked squares. The upper square carries both diagonals and both medians (one vertical, one horizontal); the lower square carries only its two diagonals.
• Upper square — with two diagonals and two medians all passing through the centre: 8 smallest triangles, plus the 4 quarter-triangles formed by joining two smallest ones across a diagonal, plus the 4 half-squares cut off by each diagonal. That gives 8 + 4 + 4 = 16.
• Lower square — with only the two diagonals: 4 small triangles around the centre plus 4 half-squares = 8.
• No triangle spans both squares, because no slanted line crosses the horizontal edge they share.
• Total = 16 + 8 = 24.

Additional Information

• The standard counts are worth memorising: a square with both diagonals contains 8 triangles; a square with both diagonals and both medians contains 16.
• When a figure is built from separate cells, count each cell with its own lines and then check only whether any line runs *through* the shared boundary. If none does, the totals simply add.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*