State True/False:

Area of an equilateral triangle of side a unit can be calculated using the formula: $(\mathrm{s}-\mathrm{a})\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})}$.

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:

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

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

In an equilateral triangle, $\mathrm{a}=\mathrm{b}=\mathrm{c}$

By Heron's formula,

Area of the given equilateral triangle $=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{a})}$

$\Rightarrow (\mathrm{s}-\mathrm{a})\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})}$

Hence, the given statement is true.