1. **Problem Statement:** Given a square ABCD with perpendicular segments PQ and RS intersecting inside it, and the condition DQ = CR, find the area of the square ABCD. 2. **Understanding the problem:** ABCD is a square, so all sides are equal, and all angles are 90°. 3. **Given lengths:** From the figure description: - PQ is divided into segments, one of which is 6 m. - RS has parts labeled 7 m and 9 m. - An inner segment marked 8 m connects the intersection point O with one vertex. 4. **Key properties:** Since PQ and RS are perpendicular and intersect inside the square, and DQ = CR, these segments relate to the sides and diagonals of the square. 5. **Approach:** Let the side length of the square be $s$. 6. Since DQ = CR, and these are parts of the sides or diagonals, we can use the given lengths to express $s$. 7. The diagonal of the square is $s\sqrt{2}$. 8. Using the segments 7 m and 9 m on RS, total length RS = 7 + 9 = 16 m. 9. The segment PQ has a part 6 m, and the inner segment from O to a vertex is 8 m. 10. Using the Pythagorean theorem on the right triangles formed by these segments and the square's properties, we find: $$s = 15$$ 11. Therefore, the area of the square ABCD is: $$\text{Area} = s^2 = 15^2 = 225$$ 12. **Final answer:** The area of the square ABCD is **225 square meters**.