Calculate the area and perimeter for triangle A:

We can use the Pythagorean theorem for the left right-angled triangle formed by the height, the side of $5.5 \text{ cm}$ (hypotenuse), and the base segment of $3.5 \text{ cm}$.
The Pythagorean theorem states $a^2 + b^2 = c^2$.

$$h^2 + (3.5 \text{ cm})^2 = (5.5 \text{ cm})^2$$ $$h^2 + 12.25 \text{ cm}^2 = 30.25 \text{ cm}^2$$ $$h^2 = 30.25 \text{ cm}^2 - 12.25 \text{ cm}^2$$ $$h^2 = 18 \text{ cm}^2$$ $$h = \sqrt{18} \text{ cm}$$ $$h \approx 4.2426 \text{ cm}$$

The formula for the area of a triangle is $A = \frac{1}{2} \times \text{base} \times \text{height}$.
The base of the triangle is $5 \text{ cm}$.

$$A = \frac{1}{2} \times 5 \text{ cm} \times \sqrt{18} \text{ cm}$$ $$A = \frac{5\sqrt{18}}{2} \text{ cm}^2$$ $$A = \frac{5 \times 3\sqrt{2}}{2} \text{ cm}^2$$ $$A = \frac{15\sqrt{2}}{2} \text{ cm}^2$$ $$A \approx \frac{15 \times 1.4142}{2} \text{ cm}^2$$ $$A \approx \frac{21.213}{2} \text{ cm}^2$$ $$A \approx 10.61 \text{ cm}^2$$

The perimeter is the sum of the lengths of all three sides of the triangle. The sides are $5.5 \text{ cm}$, $4.5 \text{ cm}$, and $5 \text{ cm}$.

$$P = 5.5 \text{ cm} + 4.5 \text{ cm} + 5 \text{ cm}$$ $$P = 15 \text{ cm}$$

The area of the triangle is $\boxed{10.61 \text{ cm}^2}$ and the perimeter is $\boxed{15 \text{ cm}}$.