Calculate Kite

The diagonals of a kite are perpendicular. Therefore, $\triangle AEB$ is a right-angled triangle. Using the Pythagorean theorem:

$$AB^2 = AE^2 + BE^2$$ $$AB^2 = 3^2 + 4^2$$ $$AB^2 = 9 + 16$$ $$AB^2 = 25$$ $$AB = \sqrt{25}$$ $$AB = 5 \text{ cm}$$

Similarly, $\triangle DEA$ is a right-angled triangle.

$$DA^2 = DE^2 + AE^2$$ $$DA^2 = 4^2 + 3^2$$ $$DA^2 = 16 + 9$$ $$DA^2 = 25$$ $$DA = \sqrt{25}$$ $$DA = 5 \text{ cm}$$

$\triangle BEC$ is a right-angled triangle.

$$BC^2 = BE^2 + CE^2$$ $$BC^2 = 4^2 + 6^2$$ $$BC^2 = 16 + 36$$ $$BC^2 = 52$$ $$BC = \sqrt{52}$$ $$BC = \sqrt{4 \times 13}$$ $$BC = 2\sqrt{13} \text{ cm}$$

$\triangle CED$ is a right-angled triangle.

$$CD^2 = CE^2 + DE^2$$ $$CD^2 = 6^2 + 4^2$$ $$CD^2 = 36 + 16$$ $$CD^2 = 52$$ $$CD = \sqrt{52}$$ $$CD = \sqrt{4 \times 13}$$ $$CD = 2\sqrt{13} \text{ cm}$$

The perimeter is the sum of all side lengths:

$$P = AB + BC + CD + DA$$ $$P = 5 + 2\sqrt{13} + 2\sqrt{13} + 5$$ $$P = 10 + 4\sqrt{13} \text{ cm}$$

Using $\sqrt{13} \approx 3.6055$:

$$P \approx 10 + 4(3.6055)$$ $$P \approx 10 + 14.422$$ $$P \approx 24.42 \text{ cm}$$

The perimeter of the kite is $\boxed{10 + 4\sqrt{13} \text{ cm}}$ or approximately $\boxed{24.42 \text{ cm}}$.

The area of a kite is given by the formula $A = \frac{1}{2} d_1 d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals.
Length of diagonal $AC = AE + CE = 3 + 6 = 9$ cm.
Length of diagonal $BD = BE + DE = 4 + 4 = 8$ cm.

$$A = \frac{1}{2} \times AC \times BD$$ $$A = \frac{1}{2} \times 9 \times 8$$ $$A = \frac{1}{2} \times 72$$ $$A = 36 \text{ cm}^2$$

The area of the kite is $\boxed{36 \text{ cm}^2}$.