Let's work through the questions provided in the image one by one.

Given Information:

1. Parking Lot Layout: A rectangular parking lot with gardens of $6 \, \text{m} \times 6 \, \text{m}$ in each corner.
2. Parking Spot Width: Each parking spot is $2.5 \, \text{m}$ wide.
3. Line Thickness: Lines separating parking spots are $7.5 \, \text{cm}$ (or $0.075 \, \text{m}$) thick.

Questions:

(a) Length of the North Side Including Gardens

• 25 Parking Spots along the North Side:
  • Each parking spot is $2.5 \, \text{m}$ wide.
  • Therefore, the length occupied by 25 parking spots = $25 \times 2.5 \, \text{m} = 62.5 \, \text{m}$.
  • Adding two $6 \, \text{m} \times 6 \, \text{m}$ gardens on both ends, the total length of the north side = $62.5 \, \text{m} + 6 \, \text{m} + 6 \, \text{m} = 74.5 \, \text{m}$.

(b) Length of the West Side Including Gardens

• 20 Parking Spots along the West Side:
  • Each parking spot is $2.5 \, \text{m}$ wide.
  • Therefore, the length occupied by 20 parking spots = $20 \times 2.5 \, \text{m} = 50 \, \text{m}$.
  • Adding two $6 \, \text{m} \times 6 \, \text{m}$ gardens on both ends, the total length of the west side = $50 \, \text{m} + 6 \, \text{m} + 6 \, \text{m} = 62 \, \text{m}$.

(c) Total Paved Area Excluding the Gardens

1. Overall Parking Lot Dimensions (with Gardens):

   • The north side total length = $74.5 \, \text{m}$.
   • The west side total length = $62 \, \text{m}$.

2. Total Area of Parking Lot (Including Gardens): $74.5 \, \text{m} \times 62 \, \text{m} = 4619 \, \text{m}^2$

3. Area of Gardens (4 corners):

   • Each garden has an area of $6 \, \text{m} \times 6 \, \text{m} = 36 \, \text{m}^2$.
   • Total area for 4 gardens = $4 \times 36 \, \text{m}^2 = 144 \, \text{m}^2$.

4. Total Paved Area (Excluding Gardens): $4619 \, \text{m}^2 - 144 \, \text{m}^2 = 4475 \, \text{m}^2$

Summary of Answers:

• (a) The length of the north side, including the gardens, is 74.5 meters.
• (b) The length of the west side, including the gardens, is 62 meters.
• (c) The total area of the paved portion of the parking lot, excluding the gardens, is 4475 square meters.

Would you like further details or have any questions on any part?

Related Questions:

1. How would the answers change if the parking spot width was increased to 3 meters?
2. What is the total length of lines separating the parking spots on the north and west sides?
3. If each parking spot could fit one car, how many cars can this parking lot accommodate?
4. How much area is occupied by the lines separating the parking spots?
5. What would be the total paved area if only two gardens were placed in the corners?

Tip:

When calculating areas or lengths with multiple components (like gardens and parking spots), separate them into individual parts first, then add or subtract as required for clarity.