How many triangles are there in the figure given below? [Refer to the figure.]

Question

How many triangles are there in the figure given below? [Refer to the figure.]

1. A. 8
2. B. 10 (Correct answer)
3. C. 12
4. D. 14

Correct Answer

Option B — 10

Detailed Solution & Explanation

The correct answer is 10.

Key Points

• Count the smallest triangles first, then the larger triangles formed by combining them.
• Adding the simple and composite triangles gives a total of 10.

Additional Information

• Count triangles by size class rather than at random: first the smallest, then those made of two smaller ones, then three, and so on until no larger triangle exists.
• Label every vertex and intersection first. An unlabelled diagram is where miscounts come from, because the same triangle gets counted twice under different descriptions.
• A useful check: the total should stay stable when you count in a different order. If two passes disagree, the smaller count usually missed a composite triangle.