How many square tiles of side 40 cm will be required to pave a footpath which is 2 m wide and surrounds a rectangular plot 80 m by 44 m ?

Answer

To solve the problem of how many square tiles of side 40 cm are required to pave a footpath that is 2 m wide and surrounds a rectangular plot of dimensions 80 m by 44 m, we will follow these steps:

### Step 1: Determine the dimensions of the outer rectangle (including the footpath).
The rectangular plot has dimensions:
- Length = 80 m
- Width = 44 m

The footpath surrounds the plot and has a width of 2 m on all sides. Therefore, we need to add 2 m to both sides of the length and width.

- Outer Length = 80 m + 2 m + 2 m = 84 m
- Outer Width = 44 m + 2 m + 2 m = 48 m

### Step 2: Calculate the area of the outer rectangle (ABCD).
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]

So, the area of the outer rectangle (ABCD) is:
\[ \text{Area}_{ABCD} = 84 \, \text{m} \times 48 \, \text{m} = 4032 \, \text{m}^2 \]

### Step 3: Calculate the area of the inner rectangle (EFGH).
The area of the inner rectangle (the plot) is:
\[ \text{Area}_{EFGH} = 80 \, \text{m} \times 44 \, \text{m} = 3520 \, \text{m}^2 \]

### Step 4: Calculate the area of the footpath.
The area of the footpath is the difference between the area of the outer rectangle and the area of the inner rectangle:
\[ \text{Area}_{\text{footpath}} = \text{Area}_{ABCD} - \text{Area}_{EFGH} \]
\[ \text{Area}_{\text{footpath}} = 4032 \, \text{m}^2 - 3520 \, \text{m}^2 = 512 \, \text{m}^2 \]

### Step 5: Calculate the area of one square tile.
The side of each square tile is given as 40 cm. To find the area in square meters, we first convert centimeters to meters:
\[ 40 \, \text{cm} = 0.4 \, \text{m} \]
Now, calculate the area of one tile:
\[ \text{Area}_{\text{tile}} = \text{side}^2 = (0.4 \, \text{m})^2 = 0.16 \, \text{m}^2 \]

### Step 6: Calculate the number of tiles required.
To find the number of tiles needed to cover the area of the footpath, we divide the area of the footpath by the area of one tile:
\[ \text{Number of tiles} = \frac{\text{Area}_{\text{footpath}}}{\text{Area}_{\text{tile}}} \]
\[ \text{Number of tiles} = \frac{512 \, \text{m}^2}{0.16 \, \text{m}^2} = 3200 \]

Thus, **3200 square tiles** of side 40 cm will be required to pave the footpath.

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