Solution :
It is given that the length of a side of a triangle is given by 'a'.
It is an equilateral triangle.
So the three sides will be of equal length and is a, a, a units.
Now the semi perimeter of the equilateral triangle is given by :
[tex]$S=\frac{a+a+a}{2}$[/tex]
[tex]$=\frac{3}{2}a$[/tex]
Therefore, using the Heron's formula, we can find the area of the equilateral triangle.
Area of the equilateral triangle is given by :
[tex]$A =\sqrt{S(S-a)(S-a)(S-a)}$[/tex]
[tex]$A =\sqrt{\frac{3a}{2}\left(\frac{3a}{2}-a\right)\left(\frac{3a}{2}-a\right)\left(\frac{3a}{2}-a\right)}$[/tex]
[tex]$A=\frac{\sqrt3}{4}a^2$[/tex] square units.
