1. **State the problem:** We need to find the perimeter of a quadrilateral with side lengths $\frac{1}{2}$ ft, $\frac{4}{9}$ ft, $\frac{4}{9}$ ft, and $\frac{1}{2}$ ft. 2. **Formula for perimeter:** The perimeter $P$ of a polygon is the sum of the lengths of all its sides. $$P = \text{side}_1 + \text{side}_2 + \text{side}_3 + \text{side}_4$$ 3. **Add the side lengths:** $$P = \frac{1}{2} + \frac{4}{9} + \frac{4}{9} + \frac{1}{2}$$ 4. **Combine like terms:** Group the $\frac{1}{2}$ terms and the $\frac{4}{9}$ terms: $$P = \left(\frac{1}{2} + \frac{1}{2}\right) + \left(\frac{4}{9} + \frac{4}{9}\right)$$ $$P = 1 + \frac{8}{9}$$ 5. **Add the whole number and fraction:** $$P = 1 + \frac{8}{9} = \frac{9}{9} + \frac{8}{9} = \frac{17}{9}$$ 6. **Convert to mixed number:** $$\frac{17}{9} = 1 \frac{8}{9}$$ **Final answer:** The perimeter is $\frac{17}{9}$ feet or $1 \frac{8}{9}$ feet.