Find the area of triangle whose sides are $5 \text{cm},12 \text{cm},13 \text{cm}$.

If a triangle has three sides, a, b, and c, semi-perimeter s, and area of triangle A, then the semi-perimeter and area of the triangle are given as:

$\mathrm{s}=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$

$\text{A}=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$

Here,$\text{a} \text{=} 5 \text{ cm,} \text{b} \text{=} 12 \text{ cm,} \text{c} \text{=} 13 \text{cm}$

Now, Semi-perimeter $\text{s}=\frac{5+12+13}{2}=15$

Then, area of triangle $=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})}$

$\Rightarrow \sqrt{15\left(10\right)\left(3\right)\left(2\right)}$

$\Rightarrow 30 {\text{cm}}^2$

Hence, the area of a triangle is $30 {\text{cm}}^2$.