The area of a circle is equal to the area of a rectangle with perimeter equal to 35 m and breadth equal to 5.5 m. What is tile area of the circle?

Options

A. 88 sq m
B. 72 sq m
C. 66 sq m
D. 54 sq m

Explanation

To find the area of the circle that is equal to the area of a rectangle with a given perimeter and breadth, we can follow these steps:

### Step 1: Understand the perimeter formula for 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 2: Substitute the known values into the perimeter formula
We know that the perimeter is 35 m and the breadth \( B \) is 5.5 m. So we can set up the equation:
\[ 2(L + 5.5) = 35 \]

### Step 3: Solve for \( L \)
First, divide both sides of the equation by 2:
\[ L + 5.5 = \frac{35}{2} = 17.5 \]
Now, subtract 5.5 from both sides to find \( L \):
\[ L = 17.5 - 5.5 = 12 \text{ m} \]

### Step 4: Calculate the area of the rectangle
The area \( A \) of a rectangle is given by:
\[ A = L \times B \]
Substituting the values of \( L \) and \( B \):
\[ A = 12 \times 5.5 = 66 \text{ m}^2 \]

### Step 5: Set the area of the circle equal to the area of the rectangle
Since the area of the circle is equal to the area of the rectangle:
\[ \text{Area of the circle} = 66 \text{ m}^2 \]

### Final Answer
The area of the circle is \( 66 \text{ m}^2 \).

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