How many triangles are there in the following figure?
2019
How many triangles are there in the following figure?
- A.
16
- B.
15
- C.
9
- D.
7
- E.
6
Attempted by 59 students.
Show answer & explanation
Correct answer: A
To find the total number of triangles, we categorize them by the number of smaller regions they contain:
1. Smallest Triangles (1 region): There are 6 small triangles surrounding the central intersection point.
2. Medium Triangles (2 regions): There are 3 triangles formed by combining two adjacent small triangles (e.g., the top half, left half, and right half relative to the center).
3. Larger Triangles (3 regions): There are 6 triangles formed by combining three small triangles (e.g., the left half of the big triangle, the right half, and the three triangles formed by vertices and the base).
4. Largest Triangle (6 regions): There is 1 large outer triangle containing all other triangles.
Total = 6 + 3 + 6 + 1 = 16 triangles.