1. **State the problem:** We are given a square ABCD with two smaller shaded squares X and Y inside it. We need to find the fraction of the area of ABCD that is shaded. 2. **Given information:** - The shaded parts X and Y are squares. - All corners of X and Y lie on the sides of ABCD or on the diagonal AC. - The sum of the shaded areas is given as $\frac{1}{2} + \frac{4}{18}$. 3. **Calculate the sum of shaded areas:** First, simplify $\frac{4}{18}$: $$\frac{4}{18} = \frac{2}{9}$$ Now add the two fractions: $$\frac{1}{2} + \frac{2}{9} = \frac{9}{18} + \frac{4}{18} = \frac{13}{18}$$ 4. **Interpretation:** The fraction $\frac{13}{18}$ represents the total shaded area as a fraction of the area of square ABCD. **Final answer:** $$\boxed{\frac{13}{18}}$$ This means that $\frac{13}{18}$ of the square ABCD is shaded.