1. **State the problem:** We are given an isosceles trapezoid KLMN with side lengths KL = $2\sqrt{2}$, LM = $\sqrt{5}$, and MN = $\sqrt{2}$. We need to find the perimeter of trapezoid KLMN. 2. **Recall the perimeter formula:** The perimeter $P$ of any polygon is the sum of the lengths of all its sides. For trapezoid KLMN, the perimeter is: $$P = KL + LM + MN + NK$$ 3. **Identify the missing side length:** We know three sides: $KL = 2\sqrt{2}$, $LM = \sqrt{5}$, and $MN = \sqrt{2}$. Since KLMN is an isosceles trapezoid, the non-parallel sides are equal. Given $LM$ and $NK$ are legs, $NK = LM = \sqrt{5}$. 4. **Calculate the perimeter:** Substitute the known values: $$P = 2\sqrt{2} + \sqrt{5} + \sqrt{2} + \sqrt{5}$$ 5. **Combine like terms:** Group the $\sqrt{2}$ and $\sqrt{5}$ terms: $$P = (2\sqrt{2} + \sqrt{2}) + (\sqrt{5} + \sqrt{5}) = 3\sqrt{2} + 2\sqrt{5}$$ 6. **Final answer:** The perimeter of trapezoid KLMN is: $$\boxed{3\sqrt{2} + 2\sqrt{5}}$$