Rahul wanted to make a temporary shelter for street dogs, by making a box like structure with tarpaulin that covers all the four sides and the top of the house. How much tarpaulin would be required to make the shelter of heigh 2.5m with base dimensions `4mxx3`m. assuming stiching margin is negligible.

Answer

To find out how much tarpaulin Rahul would need to cover the temporary shelter for street dogs, we can follow these steps:

### Step 1: Identify the dimensions of the shelter
- Length (l) = 4 m
- Breadth (b) = 3 m
- Height (h) = 2.5 m

### Step 2: Calculate the total surface area of the cuboidal shelter
The formula for the total surface area (TSA) of a cuboid is:
\[ \text{TSA} = 2(lb + bh + hl) \]
Where:
- \( l \) = length
- \( b \) = breadth
- \( h \) = height

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ \text{TSA} = 2(4 \times 3 + 3 \times 2.5 + 2.5 \times 4) \]

### Step 4: Calculate each term inside the parentheses
- \( lb = 4 \times 3 = 12 \)
- \( bh = 3 \times 2.5 = 7.5 \)
- \( hl = 2.5 \times 4 = 10 \)

### Step 5: Add the calculated values
Now, we add these values together:
\[ 12 + 7.5 + 10 = 29.5 \]

### Step 6: Multiply by 2 to find the total surface area
Now, we multiply the sum by 2:
\[ \text{TSA} = 2 \times 29.5 = 59 \, \text{m}^2 \]

### Step 7: Calculate the area of the base
The area of the base (which we do not need to cover) is:
\[ \text{Area of base} = l \times b = 4 \times 3 = 12 \, \text{m}^2 \]

### Step 8: Subtract the area of the base from the total surface area
To find the area that needs to be covered with tarpaulin, we subtract the area of the base from the total surface area:
\[ \text{Area to be covered} = \text{TSA} - \text{Area of base} = 59 - 12 = 47 \, \text{m}^2 \]

### Final Answer
Thus, the amount of tarpaulin required to cover the shelter is:
\[ \text{Area to be covered} = 47 \, \text{m}^2 \]

---