The perimeter of a sector of a circle consists of two radii and the arc connecting them.
Perimeter of sector = (Length of radius) + (Length of radius) + (Length of the arc).
Perimeter = $2r + \text{Arc Length}$.
Given: Radius ($r$) = 14 cm, and the central angle ($\theta$) = 90°.
The formula for the length of an arc is: Arc Length = $\frac{\theta}{360°} \times 2\pi r$.
Substitute the given values into the arc length formula:
Arc Length = $\frac{90}{360} \times 2 \times \pi \times 14$.
Simplify the fraction: $\frac{90}{360} = \frac{1}{4}$.
Arc Length = $\frac{1}{4} \times 28\pi$.
Arc Length = $7\pi$ cm.
Now, calculate the total perimeter of the sector:
Perimeter = $2r + \text{Arc Length} = (2 \times 14) + 7\pi$.
Perimeter = $28 + 7\pi$ cm.