1. **Problem statement:** We have a hollow shape made from four right-angled triangular tiles and four square tiles. Each triangular tile has sides 3 cm and 4 cm, and the shape is formed by placing these tiles at the corners of a larger square made of the square tiles. We need to find the perimeter of this hollow shape. 2. **Identify the triangle's hypotenuse:** Each right-angled triangle has legs 3 cm and 4 cm. Using the Pythagorean theorem, the hypotenuse $h$ is: $$h = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ cm}$$ 3. **Understand the shape:** The hollow shape is a large square with the four corners cut off by the triangular tiles. The four square tiles form the center square, and the triangles are placed at the corners. 4. **Determine the side length of the large square:** Each square tile is adjacent to two triangles. The side length of each square tile equals the length of the triangle's legs, so each square tile is 3 cm by 3 cm or 4 cm by 4 cm? Since the triangles are right-angled with legs 3 cm and 4 cm, the square tiles must be 3 cm by 3 cm or 4 cm by 4 cm? The problem states four square tiles arranged to form a larger square, so the side length of the large square is the sum of the sides of two square tiles plus the hypotenuse of the triangle. But the problem states the hollow shape is made of four triangular tiles and four square tiles arranged to form a larger square with corners cut off by the triangles. The square tiles are likely 3 cm by 3 cm or 4 cm by 4 cm? Since the triangles are placed at the corners, the side length of the large square is $3 + 4 = 7$ cm. 5. **Calculate the perimeter of the hollow shape:** The perimeter consists of the four hypotenuses of the triangles and the four sides of the square tiles between them. - Each side of the hollow shape has a segment from the square tile and a hypotenuse from the triangle. - The total perimeter is the sum of the four hypotenuses plus the four sides of the square tiles. - The length of each side of the hollow shape is $3 + 4 = 7$ cm. - The perimeter is $4 \times 7 = 28$ cm. 6. **Final answer:** The perimeter of the hollow shape is **28 cm**.