Count the number of triangles in the given figure.

- A12
- B16
- C18
- D10
Solution & Step-by-step Explanation
Let's count the triangles systematically by breaking down the layers of the figure:
1. Innermost Square with Diagonals:
A standard square divided by two intersecting diagonals contains:
* 4 small individual triangles (formed by the intersection of diagonals inside the quadrant zones).
* 4 larger triangles formed by combining two adjacent small triangles along the main diagonal division lines.
* Total in the innermost square = triangles.
2. Intermediate Tilted Square Layer:
The boundaries of the innermost square and the surrounding rotated square (diamond shape) create:
* 4 medium triangles located at the outer corners/edges of the inner square.
3. Outer Square Boundary Layer:
The intermediate tilted square meets the outer square bounding frame to form:
* 4 additional triangles at the external corners of the overall figure.
Adding all these independent sections together:
1. Innermost Square with Diagonals:
A standard square divided by two intersecting diagonals contains:
* 4 small individual triangles (formed by the intersection of diagonals inside the quadrant zones).
* 4 larger triangles formed by combining two adjacent small triangles along the main diagonal division lines.
* Total in the innermost square = triangles.
2. Intermediate Tilted Square Layer:
The boundaries of the innermost square and the surrounding rotated square (diamond shape) create:
* 4 medium triangles located at the outer corners/edges of the inner square.
3. Outer Square Boundary Layer:
The intermediate tilted square meets the outer square bounding frame to form:
* 4 additional triangles at the external corners of the overall figure.
Adding all these independent sections together: