Question

Using herons formula find the area of an equilateral triangle of side x cm

Answer 1

S = p/2
= 3x/2
$\sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{ \frac{3x}{2}( \frac{3x}{2} - x} ) {}^{3} \\ = \sqrt{ \frac{3x}{2} ( \frac{3x - 2x}{2} )} \\ = \sqrt{ \frac{3x}{2} ( \frac{x}{2} )} \\ = \sqrt{ \frac{3 {x}^{2} }{ {2}^{2} } } \\ = \frac{x \sqrt{3} }{2}$
Therefore the area of the triangle will be,
$\frac{x \sqrt{3} }{2}$