Write the Hero’s formula to calculate the area of triangle whose sides are $x, y, \mathrm{and} z$.

Concept: If a triangle has three sides $\mathrm{a}, \mathrm{b},$ and $\mathrm{c}$, semi-perimeter, $\mathrm{s}$, and area of triangle $\mathrm{A}$, then the semi-perimeter and area of the triangle are given as:

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

Area of triangle $=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$

Here, sides of the triangle are $x, y, \mathrm{and} z$.

Now, $\text{s}=\frac{x+y+z}{2}$

Area of triangle $=\sqrt{\text{s}(\text{s}-x)(\text{s}-y)(\text{s}-z)}$

Hence, the formula to find the area of the triangle with given sides is $\sqrt{\text{s}(\text{s}-x)(\text{s}-y)(\text{s}-z)}$.