Find the semi-perimeter of an equilateral triangle of side a.

If a triangle has three sides $\mathrm{a}, \mathrm{b},$ and $\mathrm{c}$, a 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 $=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$

We know that the equilateral triangle has equal sides.

Now, $\text{s}=\frac{\mathrm{a}+\mathrm{a}+\mathrm{a}}{2}=\frac{3\mathrm{a}}{2}$

Hence, the semi perimeter of an equilateral triangle of side a is $\frac{3\mathrm{a}}{2}$.