The length of the sides of a triangle are $5\text{cm}$, $12\text{cm}$ and $13\text{cm}$. Its area is:

The given side lengths are $5\text{cm}$, $12\text{cm}$, and $13\text{cm}$. We notice that these satisfy the Pythagorean theorem:
$$5^2+12^2=25+144=169=13^2$$

This confirms it is a right-angled triangle, where the perpendicular sides are $5\text{cm}$ and $12\text{cm}$, and the hypotenuse is $13\text{cm}$.

The area of a right-angled triangle is:

$$\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}=\frac{1}{2}\times 5\times 12=5\times 6=30{\text{ cm}}^2$$