一个半径为 14 cm 的圆中有三个部分被涂上阴影。这三个部分加起来占该圆的四分之一。这三个阴影部分的总周长是多少？ 取 $\pi = \frac{22}{7}$

1. Calculate the total arc length of the three shaded parts

The three parts add up to a quarter of the circle. Therefore, their combined arc length is a quarter of the circumference of the circle.
$\text{Arc length} = \frac{1}{4} \times 2 \times \pi \times r$
$\text{Arc length} = \frac{1}{4} \times 2 \times \frac{22}{7} \times 14$
$\text{Arc length} = \frac{1}{4} \times 2 \times 44 = 22 \text{ cm}$

2. Calculate the total length of the straight edges of the three shaded parts

Each shaded part is a sector, which has 2 straight edges, each equal to the radius ($14$ cm). Since there are 3 separate shaded parts, there are $3 \times 2 = 6$ straight edges in total.
$\text{Total straight edges} = 6 \times 14 = 84 \text{ cm}$

3. Calculate the total perimeter of the three shaded parts

$\text{Total perimeter} = \text{Arc length} + \text{Total straight edges}$
$\text{Total perimeter} = 22 + 84 = 106 \text{ cm}$