A rectangular garden has a length of 57m and a width Op 42 m. Calculate of how many m² will decrease the area of a garden, if the ornamental fence with a width of 60 cm will be planted incide its perimeter.

To solve this problem, we'll follow these steps:

1. **Calculate the original area of the garden:**
   - The length of the garden is \( 57 \, \text{m} \).
   - The width of the garden is \( 42 \, \text{m} \).
   - The original area \( A_{\text{original}} \) is given by:
     \[
     A_{\text{original}} = \text{length} \times \text{width} = 57 \, \text{m} \times 42 \, \text{m} = 2394 \, \text{m}^2
     \]

2. **Determine the new dimensions after planting the fence:**
   - The width of the fence is \( 60 \, \text{cm} \), which is \( 0.6 \, \text{m} \).
   - Since the fence is planted inside the perimeter, it will decrease the length and width of the garden.
   - New length \( L_{\text{new}} = 57 \, \text{m} - 2 \times 0.6 \, \text{m} = 57 \, \text{m} - 1.2 \, \text{m} = 55.8 \, \text{m} \).
   - New width \( W_{\text{new}} = 42 \, \text{m} - 2 \times 0.6 \, \text{m} = 42 \, \text{m} - 1.2 \, \text{m} = 40.8 \, \text{m} \).

3. **Calculate the new area of the garden:**
   - The new area \( A_{\text{new}} \) is:
     \[
     A_{\text{new}} = L_{\text{new}} \times W_{\text{new}} = 55.8 \, \text{m} \times 40.8 \, \text{m} = 2274.24 \, \text{m}^2
     \]

4. **Calculate the decrease in the area:**
   - The decrease in area \( \Delta A \) is:
     \[
     \Delta A = A_{\text{original}} - A_{\text{new}} = 2394 \, \text{m}^2 - 2274.24 \, \text{m}^2 = 119.76 \, \text{m}^2
     \]

So, the area of the garden will decrease by **119.76 square meters**.

Do you want any details or have any questions about the calculations? 

Here are 5 related questions:
1. How would the area change if the fence width was doubled?
2. What would be the new area if the fence was only placed along the length?
3. How does the area decrease change if the garden's dimensions were increased by 10%?
4. How would the garden's perimeter change after the fence is planted?
5. If the garden had an irregular shape, how would the decrease in area be calculated?

**Tip:** When dealing with area reductions, always account for changes on all sides if the reduction is uniform around the perimeter.

Learn how to calculate the decrease in area of a rectangular garden when an ornamental fence is planted inside its perimeter. Step-by-step solution provided, covering geometry and area calculations. Suitable for Grades 7-9.

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