The perimeter of a sector of angle `90^(@)` , whose radius is 44 cm , is ________.

Answer

To find the perimeter of a sector of a circle with a central angle of \(90^\circ\) and a radius of \(44\) cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components of the Perimeter**:
The perimeter of a sector consists of two straight sides (the radii) and the arc length.

2. **Calculate the Length of the Arc**:
The formula for the arc length \(L\) of a sector is given by:
\[ L = \frac{\theta}{360^\circ} \times 2\pi r \]
where \(\theta\) is the angle of the sector in degrees and \(r\) is the radius.

For our problem:
- \(\theta = 90^\circ\)
- \(r = 44 \, \text{cm}\)

Plugging in the values:
\[ L = \frac{90}{360} \times 2\pi \times 44 \]

3. **Simplify the Arc Length Calculation**:
\[ L = \frac{1}{4} \times 2\pi \times 44 \]
\[ L = \frac{88\pi}{4} = 22\pi \, \text{cm} \]

4. **Calculate the Total Perimeter**:
The total perimeter \(P\) of the sector is the sum of the lengths of the two radii and the arc length:
\[ P = 2r + L \]
Substituting the values:
\[ P = 2 \times 44 + 22\pi \]
\[ P = 88 + 22\pi \, \text{cm} \]

5. **Approximate \(\pi\)**:
Using \(\pi \approx \frac{22}{7}\):
\[ P \approx 88 + 22 \times \frac{22}{7} \]
\[ P \approx 88 + \frac{484}{7} \]
\[ P \approx 88 + 69.14 \approx 157.14 \, \text{cm} \]

### Final Answer:
The perimeter of the sector is approximately \(157.14 \, \text{cm}\).