City Park Playground Map: Calculate perimeters and connect shapes from smallest to largest.

Based on the analysis of the "City Park Playground Map," here is the solution to the problem.

The task requires calculating the perimeter of each colored rectangle and then connecting them in order from the smallest to the largest perimeter. The perimeters are calculated using the formula P = 2 * (length + width), where the length and width are measured in grid units.

Here are the perimeters for each shape:

1. Small Red Square: 1 unit wide x 1 unit high. Perimeter = 2 * (1 + 1) = 4 units.
2. Pink Square (Bottom): 2 units wide x 2 units high. Perimeter = 2 * (2 + 2) = 8 units.
3. Blue Square: 3 units wide x 3 units high. Perimeter = 2 * (3 + 3) = 12 units.
4. Purple Rectangle: 3 units wide x 4 units high. Perimeter = 2 * (3 + 4) = 14 units.
5. Green Square: 4 units wide x 4 units high. Perimeter = 2 * (4 + 4) = 16 units.
6. Light Blue Rectangle: 6 units wide x 3 units high. Perimeter = 2 * (6 + 3) = 18 units.
7. Orange Rectangle: 2 units wide x 8 units high. Perimeter = 2 * (2 + 8) = 20 units.
8. Large Yellow Rectangle: 7 units wide x 5 units high. Perimeter = 2 * (7 + 5) = 24 units.
9. Pink Rectangle (Top): 4 units wide x 1 unit high. Perimeter = 2 * (4 + 1) = 10 units.

Now, ordering the shapes by their perimeter from smallest to largest:

1. Red Square (4 units)
2. Pink Square (Bottom) (8 units)
3. Pink Rectangle (Top) (10 units)
4. Blue Square (12 units)
5. Purple Rectangle (14 units)
6. Green Square (16 units)
7. Light Blue Rectangle (18 units)
8. Orange Rectangle (20 units)
9. Large Yellow Rectangle (24 units)

Therefore, to complete the task, you should draw a path that starts at the small red square, then connects to the pink square at the bottom, then to the pink rectangle at the top, then to the blue square, then to the purple rectangle, then to the green square, then to the light blue rectangle, then to the orange rectangle, and finally ends at the large yellow rectangle.