1. **Problem statement:** We have two identical isosceles right-angled triangles, each containing a shaded square or rectangle. The area of the shaded square in diagram A is 50 cm². We need to find the area of the shaded square in diagram B. 2. **Understanding the problem:** Both triangles are identical, so their sides and angles are the same. Diagram A shows a smaller square near the top vertex, and diagram B shows a larger vertical rectangle (which is also a square since it's shaded as such) inside the triangle. 3. **Key properties:** - In an isosceles right-angled triangle, the legs are equal, and the hypotenuse is $\sqrt{2}$ times a leg. - The shaded square in diagram A is inside the triangle, touching the sides. 4. **Relating the squares:** - The square in diagram A has area 50 cm², so its side length is $\sqrt{50} = 5\sqrt{2}$ cm. 5. **Using similarity and geometry:** - Since the triangles are identical, the ratio of the sides of the squares relates to the triangle's dimensions. - The square in diagram B is larger and positioned differently but still inside the same triangle. 6. **Finding the area of the shaded square in diagram B:** - The problem implies the square in diagram B is twice the side length of the square in diagram A (due to the vertical extension from base to midline height). - Therefore, the side length of the square in diagram B is $2 \times 5\sqrt{2} = 10\sqrt{2}$ cm. 7. **Calculate the area:** $$\text{Area} = (10\sqrt{2})^2 = 10^2 \times (\sqrt{2})^2 = 100 \times 2 = 200 \text{ cm}^2$$ **Final answer:** The area of the shaded square in diagram B is 200 cm².