Question

Using Heron's formula, find the area of an equilateral triangle of side ${}^{\prime }{a}^{\prime }$ unit.

Answer 1

The sides of triangle are $a,a,a$ units

$s=\frac{a+a+a}{2}=\frac{3a}{2}$

Using Heron's formula

Area of equilateral triangle is $\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{\frac{3a}{2}\times \frac{a}{2}\times \frac{a}{2}\times \frac{a}{2}}=\frac{\sqrt{3}}{2}{a}^2$