Second method: Using Heron Formula

Firstly we find the value of the perimeter and then we divide it by 2.

P = a + a + a

P = 3a

$\displaystyle p=\frac{3a}{2}$

Then, we apply the formula

$\displaystyle A=\sqrt{p(p-a)(p-a)(p-a)}$

$\displaystyle A=\sqrt{\frac{3a}{2}(\frac{3a}{2}-a)(\frac{3a}{2}-a)(\frac{3a}{2}-a)}$

$\displaystyle A=\sqrt{\frac{3a}{2}(\frac{3a}{2}-\frac{2a}{2})(\frac{3a}{2}-\frac{2a}{2})(\frac{3a}{2}-\frac{2a}{2})}$

$\displaystyle A=\sqrt{\frac{3a}{2}(\frac{a}{2})(\frac{a}{2})(\frac{a}{2})}$

$\displaystyle A=\sqrt{\frac{3{{a}^{4}}}{16}}$

$\displaystyle A=\frac{{{a}^{2}}\sqrt{3}}{4}$

As you can see we get the same result but you can use whichever method looks more easy to remember or just simply learn it by heart that in a equilateral triangle the area it’s always

$\displaystyle A=\frac{{{a}^{2}}\sqrt{3}}{4}$