How many triangles are there in the following figure?

How many triangles are there in the following figure?

1. A
19
2. B
21
3. C
27
4. D
48

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Solution:

Concept: Consider 4 levels of the triangles. Count the small triangles from every 4 levels. Now manage each level like levels and get the no. of triangles. To get the total number of triangles, we have to add all three together.
At the first level =1 triangle
Second level =3 triangles
The third level =5 triangles
The fourth level = 7 triangles
Merging level (1, 2) , then (1, 2, 3) and then (1, 2, 3, 4): 3 triangles Merging levels (2, 3): 2 triangles
Merging levels 3 and 4: 4 triangles
Merging levels 2, 3, and 4 together: 2 triangles.
So, a total number of triangles =1+3+5+7+3+2+4+2=27.
Thus, there are a total of 27 triangles.
Hence, the correct answer is option (3) .

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