1. **State the problem:** We need to find the area of the square given the information about the two triangles inside it and one side length. 2. **Analyze the given information:** The square is divided by its diagonals into four right triangles. Two of these triangles have areas 30 u^2 and 10 u^2. 3. **Recall the formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 4. **Important property:** The diagonals of a square are equal in length and bisect each other at right angles. 5. **Use the side length:** One side of the square is given as 4 u. 6. **Calculate the area of the square:** The area of a square is $$\text{Area} = \text{side}^2$$ Substitute the side length: $$4^2 = 16$$ 7. **Check consistency with triangle areas:** The total area of the square is the sum of the areas of the four triangles formed by the diagonals. The two given triangles sum to 40 u^2, so the other two must also sum to 40 u^2, making the total 80 u^2, which contradicts the side length area. 8. **Conclusion:** Since the side length is 4 u, the area of the square is $$16\, u^2$$ **Final answer:** $$\boxed{16\, u^2}$$