Question

The Height Of An Equilateral Triangle measures 9 root 3 so find the area of the triangle

Answer 1

The area of an equilateral triangle is


$area = \frac{ \sqrt{3} }{4} \times {a}^{2}$
where a is the side of the equilateral triangle

The height of triangle is
$h = \frac{ \sqrt{3} }{2} \times a$
which implies
$a = \frac{2}{ \sqrt{3} } \times h$
substituting in area, we get
$area = \frac{ {h}^{2} }{ \sqrt{3} }$
hence area will be
$81 \sqrt{3}$