The perimeter of a circular plate is 132 cm. Find its area

Answer

To find the area of a circular plate given its perimeter, we can follow these steps:

### Step 1: Understand the relationship between perimeter and radius
The perimeter (circumference) of a circle is given by the formula:
\[ C = 2\pi r \]
where \(C\) is the circumference and \(r\) is the radius.

### Step 2: Substitute the given perimeter into the formula
We know the perimeter of the circular plate is 132 cm. Therefore, we can set up the equation:
\[ 2\pi r = 132 \]

### Step 3: Solve for the radius \(r\)
To find \(r\), we can rearrange the equation:
\[ r = \frac{132}{2\pi} \]
Substituting \(\pi\) with \(\frac{22}{7}\):
\[ r = \frac{132}{2 \times \frac{22}{7}} = \frac{132 \times 7}{44} \]
Now, simplifying:
\[ r = \frac{924}{44} = 21 \text{ cm} \]

### Step 4: Calculate the area of the circle
The area \(A\) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting \(r = 21\) cm and \(\pi = \frac{22}{7}\):
\[ A = \frac{22}{7} \times (21)^2 \]
Calculating \(21^2\):
\[ 21^2 = 441 \]
Now substituting back:
\[ A = \frac{22}{7} \times 441 \]

### Step 5: Simplify the area calculation
To simplify:
\[ A = \frac{22 \times 441}{7} \]
Calculating \(441 \div 7 = 63\):
\[ A = 22 \times 63 \]
Now calculating \(22 \times 63\):
\[ A = 1386 \text{ cm}^2 \]

### Final Answer
The area of the circular plate is:
\[ \boxed{1386 \text{ cm}^2} \]

---