Find the radius of the circle.

The perimeter (circumference) of the circle is given as 88 cm.
The formula for the circumference of a circle is $C = 2\pi r$.
We are given $C = 88$ cm and $\pi = \frac{22}{7}$.

$$88 = 2 \times \frac{22}{7} \times r$$ $$88 = \frac{44}{7} r$$

To find $r$, multiply both sides by $\frac{7}{44}$:

$$r = 88 \times \frac{7}{44}$$ $$r = 2 \times 7$$ $$r = 14 \text{ cm}$$

The chord AB subtends an angle of $70^\circ$ at the centre of the circle. Let the centre be O.
In $\triangle OAB$, $OA = OB = r = 14$ cm.
We can use the formula for the length of a chord: $AB = 2r \sin\left(\frac{\theta}{2}\right)$.
Here, $r = 14$ cm and $\theta = 70^\circ$.

$$AB = 2 \times 14 \times \sin\left(\frac{70^\circ}{2}\right)$$ $$AB = 28 \sin(35^\circ)$$

Using a calculator for $\sin(35^\circ)$:

$$\sin(35^\circ) \approx 0.573576436$$ $$AB = 28 \times 0.573576436$$ $$AB \approx 16.06013999$$

Rounding to three decimal places:

$$AB \approx 16.060 \text{ cm}$$

The length of the chord AB is $\boxed{16.060 \text{ cm}}$.

The formula for the area of a sector is $A_{\text{sector}} = \frac{\theta}{360^\circ} \times \pi r^2$.
Here, $\theta = 70^\circ$, $r = 14$ cm, and $\pi = \frac{22}{7}$.

$$A_{\text{sector}} = \frac{70}{360} \times \frac{22}{7} \times (14)^2$$ $$A_{\text{sector}} = \frac{7}{36} \times \frac{22}{7} \times 196$$ $$A_{\text{sector}} = \frac{22 \times 196}{36}$$ $$A_{\text{sector}} = \frac{22 \times 49}{9}$$ $$A_{\text{sector}} = \frac{1078}{9}$$ $$A_{\text{sector}} \approx 119.777777... \text{ cm}^2$$

The formula for the area of a triangle with two sides and the included angle is $A_{\triangle} = \frac{1}{2}ab\sin(C)$.
In $\triangle OAB$, $OA = OB = r = 14$ cm, and the included angle $\angle AOB = 70^\circ$.

$$A_{\triangle OAB} = \frac{1}{2} r^2 \sin(\theta)$$ $$A_{\triangle OAB} = \frac{1}{2} (14)^2 \sin(70^\circ)$$ $$A_{\triangle OAB} = \frac{1}{2} \times 196 \times \sin(70^\circ)$$ $$A_{\triangle OAB} = 98 \sin(70^\circ)$$

Using a calculator for $\sin(70^\circ)$:

$$\sin(70^\circ) \approx 0.939692621$$ $$A_{\triangle OAB} = 98 \times 0.939692621$$ $$A_{\triangle OAB} \approx 92.109876858 \text{ cm}^2$$

The area of the minor segment is the area of the sector OAB minus the area of the triangle OAB.

$$A_{\text{segment}} = A_{\text{sector}} - A_{\triangle OAB}$$ $$A_{\text{segment}} = \frac{1078}{9} - 98 \sin(70^\circ)$$ $$A_{\text{segment}} \approx 119.777777... - 92.109876858$$ $$A_{\text{segment}} \approx 27.667900142 \text{ cm}^2$$

Rounding to three decimal places:

$$A_{\text{segment}} \approx 27.668 \text{ cm}^2$$

The area of the minor segment is $\boxed{27.668 \text{ cm}^2}$.