Find the number of triangles in the figure.
- A
- B
- C
- D
Solution & Step-by-step Explanation
Let's count the triangles systematically in the given geometrical pattern:
1. Inside the central inner square:
The square is divided by vertical, horizontal, and diagonal intersection lines.
* Individual single smallest triangles =
* Triangles formed by combining two adjacent small triangles (making up half of the inner square) =
Total triangles inside the inner square =
2. Outer corner triangles:
The inner square is enclosed within an outer diamond-shaped square, forming one distinct triangle at each corner:
* Top corner triangle =
* Bottom corner triangle =
* Left corner triangle =
* Right corner triangle =
Total outer corner triangles =
3. Grand Total:
1. Inside the central inner square:
The square is divided by vertical, horizontal, and diagonal intersection lines.
* Individual single smallest triangles =
* Triangles formed by combining two adjacent small triangles (making up half of the inner square) =
Total triangles inside the inner square =
2. Outer corner triangles:
The inner square is enclosed within an outer diamond-shaped square, forming one distinct triangle at each corner:
* Top corner triangle =
* Bottom corner triangle =
* Left corner triangle =
* Right corner triangle =
Total outer corner triangles =
3. Grand Total: