The height of an equilateral triangle measures 9 cm.

Height of the equilateral triangle = 9 cm
Thus, we have:

Height $=\frac{\sqrt{3}}{2} \times$ Side

$\Rightarrow 9=\frac{\sqrt{3}}{2} \times$ Side

$\Rightarrow$ Side $=\frac{18}{\sqrt{3}}=\frac{18}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=6 \sqrt{3} \mathrm{~cm}$

Also,

Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$

$=\frac{\sqrt{3}}{4} \times(6 \sqrt{3})^{2}$

$=\frac{108}{4} \sqrt{3}$

$=27 \sqrt{3}$

$=46.76 \mathrm{~cm}^{2}$