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 complex figure:
1. Inside the innermost square box with intersecting diagonals:
When a square is divided by two diagonals, the short trick formula is: .
* Number of individual smallest triangles inside =
* Total triangles inside this inner square =
2. Triangles formed in the outer layer between the inner square and outer rotated square (rhombus structure):
* There are 4 corners/sides forming individual triangles directly pointing outwards.
* Number of these medium triangles =
3. Composite triangles formed by joining sections:
* Combining the outer triangular extensions with adjacent lines forms larger triangles. Let's look at the standard symmetrical count for this embedded structure, which yields an additional large triangles along the main axes.
Adding them together:
1. Inside the innermost square box with intersecting diagonals:
When a square is divided by two diagonals, the short trick formula is: .
* Number of individual smallest triangles inside =
* Total triangles inside this inner square =
2. Triangles formed in the outer layer between the inner square and outer rotated square (rhombus structure):
* There are 4 corners/sides forming individual triangles directly pointing outwards.
* Number of these medium triangles =
3. Composite triangles formed by joining sections:
* Combining the outer triangular extensions with adjacent lines forms larger triangles. Let's look at the standard symmetrical count for this embedded structure, which yields an additional large triangles along the main axes.
Adding them together: