A path of uniform width 2m runs around the inside of a square field of side 20m. Find the area of the path.

Answer

To find the area of the path that runs around the inside of a square field, we can follow these steps:

### Step 1: Understand the dimensions of the square field
The side of the square field is given as 20 meters.

### Step 2: Calculate the area of the outer square
The area of a square is calculated using the formula:
\[ \text{Area} = \text{side}^2 \]
For the outer square:
\[ \text{Area of outer square} (A_1) = 20^2 = 400 \, \text{m}^2 \]

### Step 3: Determine the dimensions of the inner square
Since the path has a uniform width of 2 meters running around the inside, we need to subtract this width from both sides of the square. Therefore, the side length of the inner square is:
\[ \text{Side of inner square} = 20 - 2 - 2 = 16 \, \text{m} \]

### Step 4: Calculate the area of the inner square
Using the same area formula for the inner square:
\[ \text{Area of inner square} (A_2) = 16^2 = 256 \, \text{m}^2 \]

### Step 5: Calculate the area of the path
The area of the path is the difference between the area of the outer square and the area of the inner square:
\[ \text{Area of the path} = A_1 - A_2 = 400 - 256 = 144 \, \text{m}^2 \]

### Final Answer:
The area of the path is **144 m²**.

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