1. The problem is to find the total number of triangles in a large square subdivided into a 5x5 grid with diagonal lines from each corner and additional diagonals in the central 3x3 square. 2. First, understand the structure: The large square is divided into 25 smaller squares (5 rows and 5 columns). 3. Each small square can be divided into triangles by its diagonals. The large square has diagonals from corner to corner, creating large triangles and smaller triangles inside. 4. The central 3x3 square has two additional diagonals, further subdividing those 9 squares into smaller triangles. 5. Count triangles in each part: - Triangles formed by the large square's diagonals: The two main diagonals divide the large square into 4 large triangles. - Each of the 25 small squares without extra diagonals has 2 triangles (from one diagonal). - The central 3x3 square has 9 squares, each with 2 diagonals, dividing each small square into 4 triangles. 6. Calculate: - Total small squares: 25 - Central 3x3 squares: 9 - Outer squares (25 - 9) = 16 - Triangles in outer squares: $16 \times 2 = 32$ - Triangles in central squares: $9 \times 4 = 36$ - Large triangles from main diagonals: 4 7. Total triangles = triangles in outer squares + triangles in central squares + large triangles $$32 + 36 + 4 = 72$$ 8. Therefore, the total number of triangles in the image is $72$.