Find the perimeter of the trapezoid with these vertices. \[ (2,2),(-5,2),(-2,-5),(-5,-5) \] Give an exact answer (not a decimal approximation). Simplify your answer as much as possible.

To find the perimeter of the trapezoid, we first choose an order for the vertices so that the sides form a closed, non‐intersecting shape with one pair of parallel sides. Notice that the points (2,2) and (–5,2) share the same y‑coordinate, as do the points (–2,–5) and (–5,–5). This tells us that the segments connecting (2,2) to (–5,2) and (–5,–5) to (–2,–5) are horizontal and thus parallel. These segments can serve as the bases of the trapezoid. A convenient order for the vertices is:   (2,2) → (–5,2) → (–5,–5) → (–2,–5) → back to (2,2). Now, we calculate the distance between each pair of consecutive points: 1. From (2,2) to (–5,2):   Since the y‑coordinate is the same, the distance is the difference in x‑coordinates:   Distance = |2 – (–5)| = 7. 2. From (–5,2) to (–5,–5):   Now the x‑coordinate is constant, so the distance is the difference in y‑coordinates:   Distance = |2 – (–5)| = 7. 3. From (–5,–5) to (–2,–5):   Here the y‑coordinate is the same, so the distance is:   Distance = |(–5) – (–2)| = 3. 4. From (–2,–5) back to (2,2):   Use the distance formula:   Distance = √[(2 – (–2))² + (2 – (–5))²]        = √[(4)² + (7)²]        = √(16 + 49)        = √65. Finally, add the side lengths to find the perimeter: Perimeter = 7 + 7 + 3 + √65 = 17 + √65. Thus, the exact perimeter of the trapezoid is 17 + √65.