The problem involves finding the area of a path surrounding a rectangular field. Here's the breakdown:

Step 1: Dimensions of the field

• The field itself is a rectangle measuring 20 meters by 12 meters.

Step 2: Dimensions of the outer rectangle (including the path)

• The path is 3 meters wide around the entire field. This means the total length and width of the outer rectangle (field + path) are:
  • Length of the outer rectangle = $20 + 2 \times 3 = 26$ meters
  • Width of the outer rectangle = $12 + 2 \times 3 = 18$ meters

Step 3: Areas

• Area of the outer rectangle (including the path) = $26 \times 18 = 468$ square meters
• Area of the field (inner rectangle) = $20 \times 12 = 240$ square meters

Step 4: Area of the path

The area of the path is the difference between the area of the outer rectangle and the area of the field: $\text{Area of the path} = 468 - 240 = 228 \, \text{square meters}$

Thus, the area of the path is 228 square meters.

Would you like any more details or explanations? Here are some related questions:

1. How do we calculate the area of complex shapes?
2. How would the area change if the path width were different?
3. How do different units affect area calculation?
4. Can we calculate perimeter similarly to area?
5. How do we calculate the area for non-rectangular paths?

Tip: For problems involving surrounding areas like paths, always add the width of the path to both sides to find the dimensions of the outer shape.