The perimeter of the floor of a room is 18 m and its height is 3 m. What is the area of 4 walls of the room?

Options

A. `21m^(2)`
B. `42m^(2)`
C. `54m^(2)`
D. `108m^(2)`

Answer

To find the area of the four walls of the room, we can follow these steps:

### Step 1: Understand the given information
- The perimeter of the floor of the room is 18 meters.
- The height of the room is 3 meters.

### Step 2: Use the formula for the perimeter of a rectangle
The perimeter \( P \) of a rectangle is given by the formula:
\[ P = 2(L + B) \]
where \( L \) is the length and \( B \) is the breadth.

### Step 3: Set up the equation with the given perimeter
Since the perimeter is given as 18 meters:
\[ 2(L + B) = 18 \]

### Step 4: Simplify the equation to find \( L + B \)
Divide both sides of the equation by 2:
\[ L + B = \frac{18}{2} = 9 \]

### Step 5: Use the formula for the area of the four walls
The area of the four walls \( A \) can be calculated using the formula:
\[ A = 2(L \times H + B \times H) \]
This can be simplified to:
\[ A = 2H(L + B) \]

### Step 6: Substitute the known values into the formula
We know the height \( H = 3 \) meters and \( L + B = 9 \) meters:
\[ A = 2 \times 3 \times 9 \]

### Step 7: Calculate the area
Now, calculate the area:
\[ A = 6 \times 9 = 54 \text{ square meters} \]

### Final Answer
The area of the four walls of the room is \( 54 \) square meters.

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